Intro and injured wild pigeon question

Hi everyone, Im a nature lover and need advice please. A week or so ago I found what looked like an injured wild pigeon/dove in my garden, I managed with the utmost care and a towel to put it in a large empty crisp box with ventilation and scrunched up newspaper at the bottom, I was afraid of cats and our dogs hurting it. I rang the RSPCA who said check it over and monitor it outside, there was no blood or anything broken it seemed but it wouldnt put weight on its right foot, so grudgingly I watched it and went to bed. Next day no sign of it so I thought it had flown off. Three days ago it was spotted under a bench, as I approached it, it was still limping and flapping its wings a little, I decided to put it under some bushes we have and put out a bit of bird seed and a little bowl of water, having kept an eye on it for a few days I saw it feeding and drinking water, and as its been sunny it came out and sat there, only creeping back in when one of us came out, it seems fine apart from the limping and not flying, I live in Wigan NW England anybody like to give me advice please? Thanks