Through the fertility clinics is one way. Remember, they can offer IUI as well as IVF, which is cheaper and less intrusive.
There are also sperm banks (in Europe, as well as UK). I do not know if they sell to individuals. But, for security, you'll want sperm that has been frozen and quarantined - I don't know how those can be transported and successfully defrosted by an individual.
Use a clinic. Sperm banks don't sell to individuals - you can buy sperm from abroad, like the USA, but you'd still have to go to a clinic to access it once you've bought it.
Warning: the UK is ludicrously expensive if you are doing it privately. I had to, because IUI is not available to me on the NHS in my area.
DP and I did some searching and eventually selected a clinic in Copenhagen where you can choose anonymous or non-anonymous sperm. With non-anon you get the full details, with anon you can still select height, hair and eye colour. They are midwife-led, super-positive, have the advantage that they all speak perfect English and a flight to Copenhagen is only 1 hr 50 mins.
Going abroad is certainly a viable option, and I second Copenhagen as a good choice. A few things to consider: - timing is everything. You are unlikely to know very far in advance WHEN you'll be going so flights will be last minute and may not be cheap - if you decide to do it as a day trip it is exhausting, especially if you don't have a suitable airport on your doorstep - your best chance of getting the timing right is if you have ultrasound scans and hcg injection. Some clinics in the UK will support this , but will cost money. You may be lucky enough to hit the timing with standard ovulation tests though. - the foreign clinic will probably still insist on you having hiv and hepatitis tests before treatment - if you haven't already, it may be worth having some fertility tests before you start treatment - just to give you an idea of where you stand and your chances of success