Varies. You have to get your licence issued with the TR before any training. With that you're in the hands of your licence issuer but they're usually pretty good.
There can be a bigish gap before starting the line training, possibly in excess of a month. In that case the company will put you back in the sim, at their expense, and let you do a few circuits.
Of course, it could all be very quick but I would expect a minimum of 2 weeks from TR issue.
You'll also be sent to a training base for the line training. This may or may not be in the UK and all costs associated with that are down to you. The company will provide free air travel for you as often as you want it. You just turn up at the gate with your ID (EMA landside pass issued in the first week at EMA) and jump on as a "Jump seater". Usually you just sit down the back like anyone else but it's known as jump seating.
Training bases I think include Stansted, Dublin, Bergamo, Hahn. There are others but I can't remember them at the moment.