Every country in the EU will have its' own rules
You need to tread carefully IMO.
I don't know of any country that lets you register a vehicle there without having an address for that country; get the guy who is selling the bike to let you use his address as part of the deal. So far as the UK is concerned, this has the effect that official mail of any type, including any fines, traffic infringement notices etc that you might incur, would go to that address in your name.
I don't know how it would work out in Belgium, but it is probably similar.
After that, the bike would be registered in BE of course, and you could look for insurance for it via BE or other EU based insurance brokers.
To transfer that registration to the UK, you would need to bring the bike into this country, get it MOTed and checked that it meets the UK regulations for construction of bikes (Single vehicle approval - SVA regs - I think it is called) and pay fees, including for a tax disc (road fund licence - RFL).
To meet the construction rules the bike would need a headlight that dips to the left OR you might get away with a cover strip over part of the headlight.
All of this will be somewhere online (try DVLA), as is the way in the UK nowadays!
The analogy is with the USA, where every State has its' own rules about vehicles.
For instance, BE used to have a tax disc for pedal cycles that was supposed to be renewed annually and displayed on the bike, and you were supposed to pay an extra tax if there was a radio fitted in your car.