As seeing how you're in the UK with crazy EU envrionmental/health laws, your mileage may vary on what you can pcan get.
Bog-standard, 1mm 60/40 rosin core, which you can find anywhere, should be sufficent for the work you'll be doing but my instructor from years ago recomended 1mm 63/36 NON-rosin solid core.
Here's why: 63/36 apperantly has the best (lowest) melting point of the lead/tin solder alloy ratios (before anyone asks, I know 63% + 36% /= 100%, It's due to a rounding error).
Non-rosin core because rosin has a lower melting/boiling point than the surrounding solder. Everytime you heat up rosin core solder, the rosin boils out first, leaving a ~3mm gap of rosin-less solder inside (gap size varies, depending on diameter). Therefore, everytime you move to a new contact point, for a brief instant, you're working with an un-rosin treated surface, which is bad.
(for those who don't know: rosin acts as an "high-tempature detergent" which cleans the metal of the intended solder contact point(s), which creates a better connection. You get it in little bottles and typically apply it to your contact points with a small brush, heat it up with the iron, let it "cook" for a moment and proceed with the soldering job itself.
You have to be careful with the stuff, it's crazy-sticky, like pine-tar on steroids (I've accidentally got my fingers stuck together and/or got my fingers stuck to the wires I was tinning, on occasion) and somewhat toxic.
Using it adds another step of work and sometimes it's a pain to work with but it makes a cleaner, more professional, solder connection)