How to resolve stalemate? Letting agent and tenant holding out for sky high repair quote.

Letting Agents

I seem to have arrived at a stalemate with my lettings agent and the tenant they found for me. The tenant has always seemed happy to keep renewing her AST for the last 3 years. But recently both agency and tenant have become uncommunicative and uncooperative. The agency began drip-feeding me with repair issues - first broken light fitting, then renewing taps and finally water stains on the ceiling from a leak from another flat. I pay for 'total management' so they have been getting their choice of tradesmen to visit the flat and give estimates. I have OK'd one, I'm still waiting to hear about the other, but the final estimate %7Bto cover over water stains on the ceiling%7D is crazily high. I have told them so, and that it's a relatively simple job to do this, having done so myself several times in my own flat. I cannot possibly afford what they are trying to charge me for this.
Now they have revealed that the tenant will not renew her AST %7Bwhich is now due%7D until all the repairs are complete - although she is still paying the rent. I am struggling to get the agency to produce other quotes for this ceiling job but they simply ignore any suggestions or questions from me that they do not like. Agency and tenant seem to be acting together even though I am the one paying for the 'total management'!
Should I get quotes from other tradesmen myself and hope they will cooperate with letting them in to do the work etc? In the longer term I may need to get a new lettings agent, but right now I'd just like to get the repairs done %7Bfor a reasonable fee%7D and renew the AST for another year. What do more experienced landlords advise?
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