Leaving agent that is a late payer

I have a property which I have leased through the same agent for the last 3 years. I have never felt like that I have received a great service, although paying a premium rate (12% plus VAT). The last few months the payments from the have been late, only by a few days, but it states on their terms and conditions that payment will be made on the last day of the month.

There has been various excuses for the late payments
i) The tenant made a card payment and this takes 14 days to clear. (Does it??)
ii) A new IT system has been installed.

Anyway, alarm bells were ringing for me and so decided to not have any further dealings with them once the tenants current short tenancy agreement came to an end. I informed them of my decision a month before the tenancy was due to end.

The last rental payment has still not been paid and the agent is asking me to pay 3 months rental income (plus VAT) as I am keeping the tenant as their terms of conditions. This is noted in the terms and conditions, I had not noticed it prior to this, but feel not only is this charge exceptionally high, it shouldn’t be valid as they have not stuck to their own terms of business.

I have spoken to another letting agent who has told me 3 months management fees would be the normal charge for this, which I would be happy to pay, but can I really be asked to pay the equivalent of 28 months management fees?

What is my best option to go forward with this? I have a young family and being threatened of being taken to court is a big worry for me.

Any advice would be appreciated, thank you.

Duncan