Well,.....I sympathise with you, and isn't it always the case that a seemingly really simple problem can often cause so much hassle and annoyance, and even more so when an, " expert ", is involved.
As far as your noise problem is concerned, there are usually two possible causes, air in the system, but I don't think that is your problem, I think your problem is what is known as water hammer, which is caused by a pressure wave in the pipes, which results in a loud bang when a tap is closed quickly, and which is a common problem which should be easy to fix by fitting an anti hammer valve, or possibly a pressure relief valve.
I will add some links below which will tell you more than any sane person would ever want or need to know about water hammer, including, in some cases, mathematical calculations, aaargh !.
" Bathroom fitter says water pressure is fine and taps have been fitted correctly. "
Hmmm, well, he would say that, wouldn't he, and, " bathroom fitter ", does not = qualified, experienced plumber and or heating engineer.
If the work was done so, " correctly ", how come the water doesn't flow properly, and there is a banging noise when you close the taps ?.
Do these people train specially to deliver these fob off lines, or does it just come naturally ?, standard British workman speak, ask him if he owns a horse and a big hat, why do you suppose there are so many TV progs about dodgy workmen ?.
Because you have a combi boiler, you don't have a hot water tank, your cold water comes directly from the mains and it is at mains pressure and it feeds your cold taps directly and it also goes directly to your boiler, your boiler then heats the hot supply and pumps it to the hot taps and radiators via the boilers own pump.
With a combi boiler, assuming that your mains stop cock is opened enough, the only time that water flow to the bathroom should be drastically reduced, is if someone turns on a tap in the kitchen, because the kitchen supply is usually the nearest point to the incoming mains water supply, so it can rob water from the bathroom supply if the kitchen taps, ( or washing machine/dishwasher ), are turned on.
So if the boilers pump is OK and if your mains pressure is OK, you should have a good water supply rate to your bathroom, I do, and I have a combi boiler, if you don't, then something is wrong, and you need to find a COMPETENT plumber, and or, heating engineer to look at your system and fix it, then give the bathroom fitter the bill.
Finding such a person is the hard part, ask everyone you know or work with if they can recommend someone, visit your local builders merchants and plumbing suppliers and ask them, see if your local council has a list of approved tradesmen.
You talk about basin taps, that means handbasin, and there is no way the water flow to the handbasin should be reduced, especially if the bath tap mixer is turned off, I assume that you meant to refer to the bath mixer tap, if you DID mean the handbasin taps, then your fitter has definitely made a hash of something.
If he was incompetent, you may have some other problems that are potentially dangerous.
Firstly, have you got a separate shower ?, because if you do, it needs to be a thermostatically controlled shower that is suitable for use with your particular make and model of boiler.
Why ?, because if it isn't, and someone turns on a kitchen tap, the cold water supply will be suddenly reduced to the shower, but the hot supply may continue to flow, albeit at a reduced rate, so there will be a risk of scalding, as the shower supply suddenly gets hotter, a thermostatically controlled shower will prevent that, provided that it is suitable for use with your boiler.
The same is true for a bath mixer tap, and for a combined bath mixer tap and shower attachment, which is why combined bath mixer taps with shower head attachments used to be illegal if fitted to a combi boiler system, but I imagine that has now changed since combi boilers have become so commonplace.
Here are some links where you should be able to get advice about this.
http://www.shower-spares.co.uk/index.html
http://www.tapcentre.com/en/
Also, don't forget Baxi, most of these boiler makers have technical departments that will often offer advice.
http://www.baxi.co.uk/contact.htm
As for your mains water pressure being OK, don't be too certain, I thought mine was, it certainly seemed to be, then I got a new boiler fitted.
The engineer was recommended by the boiler manufacturer, and he was on the ball, he checked the water pressure with his meter, and said it was low, he called the water company and they arrived when he was off site, and they checked the supply and said it was OK, I knew that was
b/s, but what could I say ?.
When he came back, he got on to them again, and they couldn't get away with fobbing him off, so they had to install a new section of supply pipe which fixed the problem, so be advised.
Now, and finally, the dreaded water hammer links.
http://www.diydoctor.org.uk/projects/noisypipes.htm
http://www.ehow.com/how_18170_eliminate-water-hammer.html
http://factsfacts.com/MyHomeRepair/PipeNoises.htm
http://www.wisegeek.com/what-is-water-hammer.htm
http://homerepair.about.com/od/plumbingrepair/ss/pipe_noises.htm
http://homerepair.about.com/b/2007/12/10/fixing-water-hammer.htm
http://home.howstuffworks.com/home-improvement/plumbing/how-to-fix-pipes5.htm
http://en.wikipedia.org/wiki/Water_hammer
http://www.plumbingsupply.com/waterhammerarresters.html
