I've had the car a month and in that time one of the rear tyres has gone flat, twice so it deffinitly is leaking. The wheel is quite corroded So I'm not sure if it's leaking that way. I last pumped it up 3 weeks ago, since then I drove it about 100 miles in the first two weeks then left it a week as I was away. Before I left it felt fine, though the tyre was a little soft if you pushed it with you hand. There is no dust cap on that wheel if it makes any difference. I didn't really check when I picked the car up so I thought the first flat might have been someone mucking around.

I'm off work till next monday so Ideally I want to sort it. there is a full size spare but I've not had a propper look as the tyre on it is a bit thin on tread.

Whats the best course of action?

Very likely to be leaking from the bead if they are corroded. Spray some lightly diluted soapy water round the rim and check for bubbles.

Thanks, I'll pump it up in a bit and see if that yeilds anything. If that is the case is it easilly repairable or will it mean a new wheel (Or the spare assuming the wheel is fine)?

It can be just a matter of removing the tyre, cleaning up any loose material around the bead and remounting. Most tyre places can help. If they are punctured instead then the cost of the repair needs to be offset against the life left in the tyre. Repairs for nails etc can only be done in the central 2/3rds of the tread. Anything outside that will mean a new tyre.

My last slow puncture was a poor wheel seal against a corroded rim. For an extra fiver on the normal tyre fit charge the guy took the tyre off, Dremeled the corrosion and then used a larger amount of that white greasy stuff. It has sorted it out quite nicely and the tyre has stayed up ever since.

I've got a couple of slow ones on different cars a can of tyre weld keeps it going for a good while but in the end the rim needs sorting

It's pumped up now, I'll go to the tyre shop when I can and get it sorted. I had a look at the spare and the wheel, though corroded it looks in better nick than the one on there, bar the tyre which has a bald shoulder so I've got to go anyway. I found a complete set on ebay with a day left, no bids and a start of £25 but typically too far away. I've got an electric pump now though at least so should be fine in the mean time.

Guy at my tyre shop doesnt charge for sorting minor corrosion out, in fact usually doesnt even mention it. Just polishes it up with a grinder and puts the new tyre on. He's sorted a few leaky rims out for me