My friend said either a belt or a bearing. He's going to check it out this week and get paid with tea.
Yes, the other two possibilities are the bearings in the motor or the drum but less likely as you say that it settles down after a minute or so. If either of those have gone then it would certainly be unusual after that sort of time and you certainly have a case under the SOGA.
The big problem with the SOGA is time. As others have said, when you go into the Currys store you will get nowhere - they will not even be aware of SOGA or pretend not to be. You will have to pursue through Currys HQ by letter - as you will need to build up records of your dealings with them because ultimately it may mean starting a small claims court case. It's going to take weeks if not months and all this time you are without a dryer. Some say to get get an independent engineers report - all fine and good but at what cost - possibly as much as a £149 dryer.
Of course you can collect all these costs, pay for a replacement or repair and then sue for damages but you could end up hurting your health.
Not saying not to do it, and in your shoes I would definitely be onto Currys and Hotpoint if the motor or drum bearings have failed but make sure it doesn't become an obsession.
As for checking the belt, it is pretty easy - there is very little to a dryer and they are easy to work with and unlike a washing machine are very light.
Essentially, there is a motor, a drum, a sprung idler wheel to tension the belt and the belt. By taking the top off you can see the top of the belt - whether it is loose or worn. You can rotate the drum by hand so you can see all of the belt. If you move to the back there may be an inspection cover near the bottom that will allow you to see the idler wheel - or you may have to tip it up or look from underneath. Check the idler sprung is working (it will move under hand pressure) and put a drop of 3in1 oil on the idler wheel at the axle. If that all looks fine I would then pop the top back on and try it again - you might find that you have cured the problem. If the belt looks fine then it could be the motor or drum bearing which is a more challenging problem.
For interest, the other part is the heating element - I've seen two types, a heft metal hoop and a fragile wire matrix (a bit like the inside of a toaster) Two common dryer faults with dryers are
1 - keeps tripping the fuse box. This is most likely a earth leakage fault in the hoop-type heating element. Replacement is cheap and pretty easy.
2 - taking longer to dry. Most dryers have two heat settings and most people just use the top one. This actually works by having two heating elements, one switched on for LOW and both switched on for HIGH. If drying is taking longer than normal then it is most likely that the heating element has failed and it is just working on one half. Again the fix is to replace the element.
Another tip - before looking at the dryer for faults, check that the vent isn't blocked and the fluff filter is clean. Either of these could cause the dryer to overheat and produce symptoms that can look like a dryer fault.
If you are reasonably mechanically-minded I would say that dryers are the easiest device to understand, work on and repair in the house - there really isn't much to them.
Cheers,
Nigel