As others have mentioned this may be more about your stamina and tenacity ( and your own calculation of your worth of your own time) than substantial doubts on the merit of your legal position.

I think you percieve you have two options. You may have a third ( at least)

1)You could claim against the travel insurer ( will they pay-that is still not clear?).

2) You could claim against BA.

However you have a third option-you claim against both.

If you claim against the travel insurer-and obtain a settlement according to the policy terms-this may still leave you with a shortfall (effectively an uninsured loss) of say £200

The travel insurer-will obtain a right of subrogation to the extent of the possibility of recovering their right of recovery in respect of your insured loss. ( They may even have an expess assignment of those rights of recovery).

However -the travel insurer-having paid out to you-what will they do?

Will they exercise that right of recovery? ( i.e will they take proceedings against BA/twist their arm in some fashion that you cannot?). Will they just write-off that recovery?

You are still left with an uninsured loss of say £200. You may still wish to pursue BA for that loss.

However you could claim for your entire loss-say £550-the travel insurer would effectively need to sue in your name anyway.

If you did that the travel insurer might expect you to account to them -to the extent of their insured loss payout-say £350.

Therefore the travel insurer would expect you to account to them-for something they might have been expecting to write -off anyway ( and without any investment of time/cost/risk on their part).

You could negotiate with the travel insurer-in these circumstances-in that you would effectively be acting as their recovery agent-by acting in you own name and doing the work yourself.

You could-for example-say to the travel insurer-I will pursue the entire loss but as I am doing the work and risk here-I wish that to be reflected.

Therefore say if you do recover the £350 insured loss-(as part of an overall recovery from BA of £550-perhaps you should only be expected to hand over 50% of the £350 ( or 20% or whatever percentage you negotiate) to you Mr Insurer.

The travel insurer gets something they might not otherwise expect to receive-and you also receive some contribution to your effort to that (joint) recovery exercise.

The overall risk as far as you are concerned is that-the whole process is drawn out a bit-as the insurance claim will be processed-and all the while your focus and interest may wane.