Not sure how many times this has been covered, but...
If you have an accident and your MOT has expired (or you forgot to get the first one), then it will not affect your insurance policy unless:
1. A defect that would be picke dup o nthe MOT (i.e. bald tyre, brakes) caused or contirbuted to the incident - braking hard in wet weather for example, or
2. If you car is written off, a reduced settlement figure may be put forward to reflect the lack of MOT.
Lack of an MOT in itself is not justification to refuse a claim unless there is a specific clause in the policy - I'm not currently aware of any