After being convicted of theft and being ordered to pay compensation to the victim (which I am doing at £20 a week), I have received a letter from the victims insurance company saying I have to reimburse them for what they have paid to the victim as well. Is this right?

In the US, yes. UK? I don't know why not.

Yes, the insurance company can sue you for the amount of money they paid out to the victim. But if you are ordered to pay the victim so much a week this would ultimately amount to double dipping you. You should be paying the insurance company unless the judge ordered you to pay the victim's deductible which would make sense in this case.

You should look at what it says in your judgment of conviction. I would expect it to order restitution to a named individual (the individual you stole from or the insurance company by name), not just a relatively vague "the victim". The insurance company is, by the way, a victim of your crime.