Handbags   (The sad, the bad and the ugly. Non-productive stuff here.)

can someone give me some advice what to do ,first i am not a cat lover ,ive allways had a dog ,since moving into a bungalow 8 months age ,there is a cat which sits under my back window ,or on the back step ,and front step ,its acommunal garden well partly some have fenced off so they have there own private garden ,i know some people throw food out either chick or bread which to me harbours rats .but the point i want advice over is ,the cat belonged to the old lady before me ,at least im under the impression it was hers she went into a care home ,and im led to believe some relatives were going to take it ,but this never happened ,would the rspca take it ,i havent the transport or cat cage to take .my family keeps saying especially my granddaughter,nan let it in your mean .but honestly i hold my hand up i dont like cats ,but wouldn want any animal suffer ,or go through any bad winter we may have .so would the rspca take it ?