Driving without a valid MOT certificate CAN'T invalidate the '3rd party' element of an insurance policy. So the good news part of my post is that you CAN'T be prosecuted for driving without insurance. (The insurer MUST pay out in respect of any valid third party claim).
The first part of the bad news is that, depending upon the wording of the policy, your insurer can refuse to pay out on any other part of the insurance cover. (i.e. if you've got 'fully comp' cover the insurer only has to pay out the '3rd party' element).
The next part of the bad news is that, although the insurer has to pay out on any third party claim (meaning that you can't be prosecuted for having no insurance), the wording of the policy might allow the insurer to seek that money back from you because you weren't driving in accordance with the policy.
Next bit of bad news: As should be obvious, you're clearly at risk of being prosecuted for driving without a valid MOT certificate.
Although you've insured through a broker, any payments from your bank will almost certainly have been paid directly to the insurance company. So if you pay by direct debit you only need to look at your bank statements (or ask your bank) to see which company you're insured with.
If you can't find out that way who you're insured with, it's going to cost you a tenner:
http://stayinsured.askmid.com/accessmypersonalinfo.html