Lack of Water Pressure in London Flat

My mother-in-law a third-storey flat in London with almost zero water pressure. We stay there when we have to be in London, and it is horrible because I can't shower the entire time I'm there.

We are going there Sunday afternoon, to attend an important dress-up do on Monday night, and I'm not looking forward to being greasy and smelly in my nice dress.

If you turn on the tap in the bath, water trickles out slowly, dribble by dribble. You could  turn the tap on, go to town in the morning and come back later in the day, and the bath would still be filling up. There is a shower hose attached to the tub, but it is useless, because there isn't enough pressure to get the water up the hose.

I also only take showers - I get very dizzy in baths.

There is no shower curtain, so I assume that my MIL prefers baths, and just waits for the tub to fill.

It also takes forever for the toilet to fill up after someone goes.

The flat has a closet with a huge water tan  that makes a lot of noise every time someone flushes the toilet or turns on a tap.

Not really clear on how to cope with this. Our flat in York is almost as high up and we have no problems with water pressure at all. We don't have our own water tank; I assume there is just one for the whole block of flats?

Have you turned the mains tap on and off a few times? That sometimes works.

A couple of questions:

1.  Are both hot and cold at the bathtub and lavatory basin of similarly low pressure and flow rate? 

2.  What is the pressure like at the cold tap on the kitchen sink by comparison?

I'm not there anymore so I'll try to remember.

Kitchen sink and bathroom sink flow seem normal. Possibly slightly less pressure than my flat in York, but nothing to complain about.

Toilet tank is incredibly slow to fill up.

If the cold tap in the kitchen seems O.K., then the incoming mains pressure is probably adequate.   The water tank in the closet might be the problem.  If the tank is only a couple of feet above the outlets it serves, then the pressure from the low head of water will be very low.  There may also be a blockage or restriction at some part of the system which is exacerbating the problem.

We'd need some more information on the plumbing arrangements to narrow it down.