Davy,
Well, if you are in the UK, you are sort of in the heart of British Israelism or Anglo Israel territory. You are right, most of the British Israel people seem to want to separate from "Christian Identity" and they do allow a whole variety of theological beliefs in their ranks. I couldn't even get their people here in the US to agree that election would be a core doctrine to any Anglo Israel believer. You need to shop carefully, and you may not be able to find a church that is in exact agreement with you on every doctrinal point, but if they hold to the basics of the faith with regard to Jesus Christ, they believe in baptism as outlined in scripture and you can get them to perform it for you in accordance with scripture, that might be your only alternative, at least at this point. You may already be familiar with these, but I list a few websites below. If you start doing a little research you may come up with an acceptable alternative church to perform the service (you might not want to mention to them that you are CI

). It really is important that you get your baptism attended to.
Orange Street Congregational Church, London
http://www.orange-street-church.org/default.asp
British Israel World Federation UK
http://www.britishisrael.co.uk/
Covenant People's Fellowship UK
http://www.covenant-peoples.com/
Infant or child baptism does not count. Yes, it would appear to be quite essential and very important that the words spoken are correct and that you undergo full immersion baptism:
Act 2:37-41
(37) Now when they heard this, they were pricked in their heart, and said unto Peter and the rest of the apostles, Brethren, what shall we do?
(38 ) And Peter said unto them, Repent ye, and be baptized every one of you in the name of Jesus Christ unto the remission of your sins; and ye shall receive the gift of the Holy Spirit.
(39) For to you is the promise, and to your children, and to all that are afar off, even as many as the Lord our God shall call unto him.
(40) And with many other words he testified, and exhorted them, saying, Save yourselves from this crooked generation.
(41) They then that received his word were baptized: and there were added unto them in that day about three thousand souls.
Obadiah 1:18 And the house of Jacob shall be a fire, and the house of Joseph a flame, and the house of Esau for stubble, and they shall kindle in them, and devour them; and there shall not be any remaining of the house of Esau; for the LORD hath spoken it.