Moving City

I reached out to Moving City having just arrived in London and in need of a home. I emailed about a few listings and promptly heard back with a call to schedule viewings.
The flat we liked was about 100pw above our budget. The agent told us the landlord was flexible and would most likely accept our lower offer. We should put one in, pay the deposit and her fees now, and if for some reason it does not get accepted, we would be refunded in full.
After a few days and multiple calls to the agent, her boss, and the office, it became clear that our offer had not been accepted. We said no problem, we found another flat with another estate agency so we would like our deposit back in order to make an offer else where.
I was taken aback when the Moving City agent said it take some time to get the deposit back. Why don’t we let her make the offer?
We said we’d already had a viewing with another company but she said no matter, she’d get us a better price (like the last place?) and throw in some «move-​in cash» on top of that.
I called my friends at the other estate agency (Square Mile) to tell them about the counteroffer. They basically told me what she was doing was illegal.
Illegal or not, this is not an agency I advise doing business with. We ultimately secured the other flat with the other company and were refunded our deposit after about 2 weeks of chasing but it was a harrowing process!