Definitely go used. You'll get way more bang-for-buck if you're working to a £300 budget.
I'd suggest starting out with a hybrid or a touring bicycle, as both will give you more flexibility in terms of use / gear range and general comfort while riding. An out-and-out road bike will always be an out-and-out road bike. A hybrid or a tourer will give you a choice of three chain rings up front and a much more useable range of ratios on the back. Plus one of the best ways of simply getting out on the bike is doing utility rides - pop to the shops, to the post office or whatever you need to do instead of taking the car. Fit mudguards and a rack, and you've got a capable do-it-all.
If you're mechanically savvy and happy to tinker, then you've definitely got more options. Look for a nice frame and then build it up how you want it. The danger there, is that you can get carried away on the parts front. Most of us here have fallen down that particular rabbit hole and spent way more than intended LOL!
As for accessories, then helmet, gloves (will protect the skin on your palms if you have an unscheduled dismount), glasses (to keep flies and dust out of your eyes), lights, mudguards. That should get you started at least.
Decathlon are a good port of call for these kinds of gubbins, and their own brand stuff is pretty good. Most of my cycling clothing and accessories come from Decathlon. If you're in Basildon, it may be worth a trip to have a mooch around the big one at Lakeside.
Also budget for a saddle. You may find the saddle that comes with whatever bike you get works for you - which in that case, you can divert those spendables back towards other bits. But there is absolutely nothing worse than cycling any sort of distance on a saddle that offends your bottom.