House sale threatened through court action

[porpoise]

Would be ever so grateful for some advice please.
Used to own flat in London (sold a few years ago).
Estate agent who let it for me put dreadful tenants in who cost me £20k in unpaid rent and legal costs. I pursued the estate agent to recoup my costs but they wriggled out of it through a loophole.
After flat sold, estate agent accidentally put just under £3500 in my bank account which I kept and spent.
They came after me a couple of years later and I've been paying them back interest free at £50 a month for the last three years. £1700-odd outstanding. There's no contract in place.
They've now put a debt collector on the case who's chasing the money plus costs.
I'm in a very poor financial situation, which I have demonstrated to them. Have a start-up business which isn't making a profit yet, quite a lot of debt and relatively high living costs (live and work at home alone).
I'm a homeowner with a mortgage.
Offered debt collector £500 as credit card payment as full and final settlement.
They responded today saying they're going to take me to court and seek to take a claim on my house and force its sale.
Are they allowed to do this? Would be so grateful for any help and advice that you can offer.
Thank you in advance.

[Amethyst]

There may be no written contract in place but there is a verbal agreement which you have been sticking to of repayment at £50 per month. If they went to court they would likely only get the same. £50 per month installments. However you don't want them to do that as you don't want ( or deserve ) a CCJ just because they have decided they want quicker payment.

DO you have a copy of this letter from this debt collector ? or was it a visit ? can you post a pic of the first letter and this threatening letter about taking your house ? ( slightly over the top ! - they couldn't if you got the debt down under £1000 anyway, and tbh no court is going to allow a sale order on this - they have so many hoops to jump through before you got anywhere near that stage you'd likely have paid it down to under £1000 with your instalments by that time anyway )

[porpoise]

Thank you ever so much for your reply. I didn't get an email notification annoyingly. Checked junk mail.
Attached are screenshots of the conversation history from the debt collector's side with some info blanked out in the interests of security (hope it isn't a problem to include the name of the debt collector).
Would be most grateful for your further help and advice.
Thank you again.

[2222]

Why does the letter say that £3000-odd is outstanding? There was an agreement to pay the £3500 off at £50 pm, which you seem to have stuck to. There does not seem any basis to load that up by another £1300. Has that been explained?