Thank you very much for the replies.

The issue is that these are my first credit cards, so necessarily have a relatively low limit. Paying the balance on them is not a problem, it’s just the physical limit that is the issue. The card I am using for the rental is just for this rental and nothing else. (I can’t use my debit card due to not quite meeting all the conditions at the counter). I have used up the available balance in its entirety for this rental (including Hertz’s extra held funds). I have LDW and LIS included in my rental.
If I then posted to the credit card the exact amount to pay it off, does that sort of free up the same amount if I were to extend the rental, or is the credit limit regardless of how much funds have been posted to the account? So right now I have say £50 remaining to use on the card, with the rental amount ‘blocking’ the rest. If I put the rental amount back on my credit card with my debit card, do I now have my full balance to play with again?

I’m not sure how they’d respond to a request to increase the credit limit as I’ve only had the card for a short time. Also I worry that such a request, if declined, may harm my (English) credit score.