you can go down your local fish shop and talk to the guys there,u will need a 25 watt heater for the tank,as small as possible so it fits in, your best option for a tank is a square or rectangle,u dont want a fish bowl as its hard to attach a heater and filter to the sides of a bowl.. for a filter you could go youtube and look at how to make your own sponge filter,they are cheap and do they job without creating alot of flow to blow the betta around the tank, youll need to buy a air pump some tubing and some sponge,total cost maybe 15 quid,or you can check a couple of fish shops and but a small filter from there..
your not gonna want a big bulky filter,im not sure if they sell the hang on back of the tank ones in the uk,it seems to be popular in america,most of the filter will hang over the back of your tank so it will give u more room in the tank for the fish..again u dont want a big bulky one,just a small one that is marked for use with a 5 or 10 gallon.and then youd prob need to baffle the outflow with some sponge so it wont blow ur betta around the tank
youll also want a lid on your tank coz some bettas might jump out and if your not around to see it you could come home to a dead betta lying on your floor. so if you do go for a hang on back filter there will need to be a section cut outof your lid for the filter to pop out through..
a little sponge filters probly your best best, check youtube and ebay