You can buy a reasonably cheap 27x1&1/4" Alloy wheel on Ebay, it may not be an exact match but will get you going again, on something that would cost you a considerable amount if you were to buy it today
I can only echo the above comments; all that you 'need' to do is to replace a wheel - it certainly doesn't warrant a restoration.
I had a Carlton Pro-Am which I very much regret selling. Sure, other bikes might be 'flashier' looking, might be fractionally lighter etc., but I've never found one that was more comfortable to ride ! (Comfort is something which should never be understated)
I've seen plenty of Pro-Ams, but I've never seen a Pro-Am with the same finish as yours; imo, it would be a shame to get it re-painted.
Oh yes, 'my' Pro-Am didn't have a Brooks saddle as an original fitting - you should find it to be very comfortable.
No doubt our resident Carlton expert (Spokesmann) will be along soon to tell you more - he is the
person to tell you about this bike.
Sort out the wheel, give it a wipe down & check over and enjoy what is left of the summer.