Can Letting Agents charge whatever they feel like for cleaning?

My partner and I rented a 2-bedroom flat via a London letting agent with a hefty deposit. Although we left the property in "good clean condition" as described in the checkout report, and hired cleaners before we left, the letting agents are trying to keep £195 for a full property clean, as the report also mentions a few minor things that weren't clean.

These include (in entirety):

Dirty washing machine drawer
Food stains in dishwasher
Taps have lime scale
Tumble dryer filter is full of fluff

Can they really charge what they like? I will concede perhaps these things were overlooked. Indeed unfortunately all appliances were brand new when we moved in so we cannot claim food stains were already in the dishwasher. But £200 to clean the whole place based on four minor items?!

In addition they want to charge £135 for repainting a few glossy white bits on a matte white kitchen wall. I swear that these areas were always there but since the check-in inventory doesn't mention them, we will have difficulty proving that. I suppose they don't need to prove it themselves?

All these items plus VAT, plus another few hundred to replace lightbulbs and repaint the living room, and we look set to lose almost half our deposit :eek:

Despite asking repeatedly for detailed invoices with a breakdown of costs and work, we are being ignored or shown invoices with just the total amounts, no breakdowns.

Is it worth raising a dispute or is the Deposit holding scheme just going to shrug in the letting agents' favour? If it helps we can also prove the letting agents did not respond to our requests for repairs or give the correct amount of notice to vacate the property - which they did solely in order to get new tenants in. No, we don't know why either, other than perhaps the new tenants get to pay higher rent...