There's basically 3 methods:
1. Using Fuel Scale Charge
2. Full cost method (where you claim a proportion of fuel, servicing etc according to the % of business/total mileage)
3. Mileage method (where you claim £0.45 per mile < 10,000 miles pa and then £0.25 > 10,000)
4. Don't claim any VAT at all
For both 2 and 3, the client MUST keep detailed mileage records. This shouldn't be that onerous these days: as long as they have a record of all their business trips, you can plug the postcodes into an online distance calculator and work out the mileage.
It's worth bearing in mind that, strictly speaking, the client should be keeping mileage records (or at least some robust evidence) if they want to claim a proportion of their motor expenses as income tax deductable business expense anyway (never mind whether they are VAT reg or not).
If they don't want to calculate the mileage, then they have only options 1 or 4 above.
You may find these links useful. Arm yourself with the information in these and then explain the options to your client and that you are merely trying to keep them out of trouble:
Good luck :)