First of all, you won't have to pay anything to the other party because you have less than comprehensive cover - I have no idea where peoplle get this idea from - third party cover means that you are covered for the third party damage, not yours. There is no reason to inspect your car, as they have rightly said that they would not be repairing your car even if you were 100% not at fault.
In regards to a 50/50, with no independent witnesses, that's all you're going to get. These claims are nightmares to deal with when there is a witness, never mind when there isn't.
Generally in these cases, only one person is telling the truth, and the insurer is going to believe their client first and foremost.
Dispute it all you want, but your insurer will not allow this to go to court given what you've told us, and it will end up getting settled regardless on a 50/50 basis.
And for the record, not every accident that occurs without witnesses is a 50/50 settlement - roundabout collisions are notoriously difficult to prove - all the other party has to say is that you dangerously undertook them on the roundabout, hence the collision - no witnesses means that their version of events is a probable as yours is. The damage would appear consistent in both scenarios - seen it far too many times.