Hello Kev, Welcome.
I think Steve's advice of checking with your local Audi dealer regarding any recorded service history is well worth following. I'm sure Steve will be better placed to know about this than me, but I think it may be useful to have the VIN (number) to hand when you contact them, as well as the registration number.
Timing belt? Those more knowledgeable on diesel engines than I, will advise you whether this is a chain or belt driven engine. Even if a chain, it may be wise not to ignore it anyway.
If a belt, it is indeed very wise to consider changing this if you cannot establish when it was last done, and indeed, even if this may not be too long ago - find out what make if belt was used. As you will know, the belt, tensioners, and water pump make up a "critical parts" application package on belt driven engines, and in my book the first choice would always, alway, be main dealer parts (at discount would be great and is usually possible). The only aftermarket belt I would consider is the one your garage mentioned - Gates. Gates are reputable and manufacture belts for motor manufacturers. Draw the line at these two Kev. If you start delving into cheaper kits then you start to lose the plot. This certainly isn't a cost-is-King job.
The quote of £160 from your local garage (not main dealer?) - is that for the supply ( of Gates kit) and fit? If so , this seems rather cheap (too cheap?) to me.
Where to beware:- OK , so you decide to go for Gates and see a kit at a great price on the Internet and decide to go for that. Beware, since these may be old stock and perhaps even older than the recommended years- change interval that Audi recommend as a change! Same with the odd Audi kits which turn up from time to time.
Water pumps. Critical part of the set up, and believe me, there are some .....p aftermarket pumps available. My advice is to just don't go there, You can get Gates kits with water pumps, but I don't have any experience of who makes the pumps for their kits, so I would be rather hesitant to go with that. For me, it would be a VAG only part, and I know they did actually do reconditioned exchange pumps.
It would probably be well worth changing the auxiliary (serpentine) belt at the same time, since if these go, they can wrap themselves around all sorts of moving parts which can lead to the timing belt jumping a tooth. Again, main dealer or Gates only.
Last point Kev. Main dealers sometimes have offers on timing belt changes so could be worth looking into that.as well.
I mentioned main dealer at discounts, and I know Rainsworth Skoda (Nottingham?) usually offer mail order discounts. No connection, and no doubt there are others.
Kind regards,
Gareth.