Finally, here is an even more important point that warrants its own paragraph. From Judaism's perspective you do not need to be a Jew to make it into heaven! Judaism teaches that the righteous of all nations shall enter the gates of heaven. You might thus first like to consider contacting a representative of the B'nei Noah movement. The movement's UK home page can be found on my UK Jewish links page under "Non-Jewish Friends".
If after investigating the B'nei Noah option you still want to convert here are a few pointers. They are only suggestions but hopefully they will allow you to avoid some of the pitfalls.
Get a good introduction to Judaism from your local library. Be sure that you really know what you are getting into. With all due respect, it is surprising how ignorant some non-Jews are about even basic Judaism. Try to ensure that the author is Orthodox because that way you are likely to get the full picture. This comment is not meant to deprecate non-Orthodox writers, but non-Orthodox Judaism does differ and you might as well start by seeing what it differs from.
Subscribe to a good Jewish weekly newspaper.
Some synagogues welcome visitors. Often this requires permission, so don't just turn up or you might experience your first disappointment (synagogues sometimes have security staff who will turn away uninvited non-members). Visitors are usually well cared for and you will not need to take anything. Dress as appropriate to a place of worship. Ladies should play safe and dress modestly (i.e. no mini-skirts, trousers, revealing tops, etc.).
If you are fortunate and live in an area richly endowed with synagogues try to visit several taking in both the Orthodox and non-Orthodox ones.
Once you have, as it were, converted already in your heart make a few changes in your life. The following often come naturally, but I will mention them anyway. Try to observe kashrut (the Jewish food laws). Stop eating pig products. Avoid working on Saturday. In other words, within the limits of your knowledge live the Jewish life that your blossoming Jewish heart dictates.
It is very important before making your desire to convert known that you consider the consequences of who does the conversion.
Judaism is currently divided into Orthodox and non-Orthodox camps. These are not denominations in the Christian sense and there are signs that relations are improving, but it means that conversions by non-Orthodox rabbis are not recognised by Orthodox rabbis.
I would point out that the non-recognition of non-Orthodox conversions by Orthodox authorities is not to do with "race" as I have heard some people suggest. It is mainly to do with the Law and its interpretation. Judaism is a religion of law (one of its great strengths). Certain aspects of Jewish law have been criticised and rejected by non-Orthodox Judaism (that is what makes it non-Orthodox). If you convert, the final drama will be played out before a Beth Din (Rabbinical court) made up of three rabbis. For the Beth Din to be recognised as valid in Jewish law the three rabbis must all be righteous men. Some Orthodox rabbis would argue that non-Orthodox rabbis are not righteous men because they represent movements that have rejected a part of Jewish law and teach others to do likewise. So if they are not righteous men then their Beth Din is not valid in Jewish law and neither is a conversion made under its jurisdiction.
The foregoing is not the whole story by a long way. It could also be criticised I am sure as an oversimplification even as it is. Nonetheless, I hope that you are getting the point. Do you really want to get involved in the sorts of problems that can arise out of non-recognition of your conversion? Is it not better to secure a conversion that will be recognised by all Jewish authorities? So I would advise that if you are serious about Judaism (and I hope that you would not otherwise even contemplate conversion) approach an Orthodox authority right from the very outset.
Most synagogues belonging to the various movements within Judaism are members of a representative union. So once you have decided that it is time to make a formal approach, you could try writing to one of the unions expressing your desire. A better method would be to track down the address of a local Orthodox rabbi and write to him or you could try telephoning to make an appointment. Often address information is available in your local library. Alternatively, you could write to the appropriate synagogal union and ask them. If you do this it is best not to mention that you have conversion in mind.
The foregoing might sound a bit vague because the initial contact can sometimes be difficult, especially once it is known that you want to convert. The reluctance of Judaism to accept converts comes mainly from two considerations.
Firstly, Judaism, unlike say Christianity and Islam, is not a proselytising religion. Because it teaches that the righteous of all nations shall enter the gates of heaven, it does not have that compelling urge to rescue non-Jews from hell, damnation or whatever, that typically drives, say, certain Christians.
Secondly, there was a time when converting to Judaism was a capital offence in certain countries. This could mean both the potential convert and the rabbi involved losing their lives. This not unreasonably instilled a reluctance to convert anyone to Judaism even after the foregoing laws were repealed.
There is a requirement in Jewish law to ensure the sincerity of a potential convert. This is taken very seriously and when played out against the background of the foregoing considerations, most authorities take their time about it. Essentially, they want to be sure that you know what you are letting yourself in for and that you are doing it for sincerely religious reasons. Wanting to marry a Jewish person or migrate to Israel or even as I remember one person saying, wanting to stand with the Jews as a sign of solidary, will be seen as compromising your claim to religious sincerity. You will need to convince a rabbi of your solely religious sincerity to have any hope of acceptance.
One of the tests of a potential convert recommended by the Talmud is to politely refuse him or her. If the person keeps returning it is seen as a sign that the person at least has commitment. So be persistent. Once you have made it over the initial hurdles things really do get easier.
I hope that the foregoing will prove helpful to you. If Judaism becomes your chosen path I can only wish you n'see'ah tovah (good journey), good luck and I hope that one day we might meet in Shul.
Finally, I recommend you visit the Conversion to Judaism Home Page
at www.convert.org/ where you will find expert help.