I'm not totally up to date with the legislation around R11. but:
Regassing refrigerators is a specialised business. It needs a host of specialised equipment and, of course, the gas. Manufacturers are no longer making refrigerators with R11 (it's banned in new machines). Furthermore, any R11 that escapes, during repair, has to be captured. Allowing it into the atmosphere is a criminal offence. I beleive it is now illegal to sell even a second hand refrigerator containing R11. and I wouldn't be surprised if the regassing of them has also now been criminalised.
The regassing process itself, is inherantly, very expensive, but R11 issue will make it even more so. (I would expect a bill in excess of £200).
Looking at the price of refrigerators now, I'd say it's a write off.
All this assumes, however, that your engineer has been honest. The only way you can loose refrigerant is through a leek. This can be caused by defrosting using sharp implements, or damage to the cooling vanes at the back. Even if you do have a leak, if your machine is quite new, it is unlikely to have R11 gas.
If your frige is quite old and the motor still runs when turned on, chances are he's right.