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Personally I'd go for a well known brand of tent rather than a supermarket cheapy as they don't tend to be as well made and have a reputation for leaking but for £12 it may be a case of stick it up in the garden and see what it's like, put the hose pipe on it and check for leaks.  At least with Tesco you will be able to take it back to the store if there's something wrong with it. 

As to what else you need, with no car you'll be wanting to travel light so a kit with spare bits for the tent in is essential, spare pole section, tape to mend tears / wrap up poles, and a tube of sealant.  Something to sleep on and in (good sleeping bag essential), something to cook on, perhaps a trangia and mess tins to eat out of with the cutlery sets that clip together. and light weight layers of clothes that are easy to wash and quick to dry (go to decathlon for T shirts and fleeces). 

Hope that's some help

Somewhere on this site think it might be somewhere on the features / tips section there's a load of camping recipies.  Don't forget if you get a bbq (disposable ones are fine) you can do meat etc on that and have a pan of veggies / pasta / rice etc to accompany it on your gas burner. 

If you find a site with a fridge / freezer that you can use you're laughing for keeping your food fresh, just remember to mark everything that's yours.  A stream makes a good beer can / milk bottle cooler too.