Air Con blowing warm air after recharging/refilling

From the described symptoms it sounds to me that it's been overfilled. The compressor is kicking in - encountering the problem and switching back off. I'd avoid attempting to use it until you can get the system checked, some systems will shut off before damage can occur whereas others aren't quite so quick and depending on how badly it's overfilled you can end up destroying the compressor. The fact that it's vibrating noticeably would lead me to fear the latter (one of the symptoms of an overfill is that the refrigerant is in a liquid state where it should be gaseous and unpleasantness can ensue)

Take it to a decent garage that does A/C work and get them to check the pressure levels properly - I have to be honest I don't have a high opinion of Halfords "technicians" all to often they are actually retail staff with minimal training or experience. I've had the misfortune to (attempt) to use them for some small things in the past (e.g. changing a bulb, fitting wipers) when I've decided that I can't be bothered to muck about doing it myself in the cold/rain etc. I've literally never had them succeed. It might just be my local branch but I'm sure as hell not going to be letting a company whose staff can't even fit a wiper blade near anything like an A/C system.

That's clearly an AC compressor cycling its clutch on and off. Car looks pretty new and this means it's definitely cycling on high pressure, meaning that whoever serviced the car seriously overfilled it with AC refrigerant. Next time, check the refrigerant amount for your car (on my Vauxhall it's written on a sticker found under the hood) and actually tell the AC guy the grams of refrigerant that your car's AC requires. Might end up annoying the AC guy, but that's how you avoid being either overfilled or underfilled (and both things are highly detrimental).

Also, if your system has a leak, you're better off searching for leaks by yourself and then going to the shop with the original spare parts in your hands. Check the entire AC system for anything green and oily that glows to a UV lamp, and for anything that smells like fresh paint.