Replacing tap washers on older taps

This is not such a new topic as further help needed.
We have now found that our problem is not the water pump, but simply the washers. However, how do we access the washers to replace them?
The fixtures on our 1998 VW Topaz are probably original, and don't have the cartridges that newer taps have (we think).
Both taps leak under pressure, so both need washer replacement - I think I need to remove the red/blue 'plugs' on the kitchen tap, but I'd value any advice before I do something I might regret later! Here are the taps in question:

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Thanks.  Alan

Alan, well done for identifying the cause. i've replaced identical sink taps on a yacht before and as you say you need to carefully prise off the red and blue inserts which will then allow you to locate the screws beneath. Undo them (anticlockwise) whilst holding the tap. Be careful with the clear plastic taps as they can sometimes fracture when being undone. There's a chrome plastic part under the clear piece which pulls off. Then its a case of using two wrenches one to hold the metal body of the tap whilst you turn (anticlockwise) the valve nut underneath. They should undo easily enough. The whole valve will then come out and you can see the rubber washer at the bottom. Replacement is either a push fit or held by another smaller nut. The washers cost, well washers However look inside the pipe where the tap washer screws in and make sure the surface the washers screw onto is smooth. Consider if you wish to replace just the washers or the whole valve, they can be quite cheap on the internet. When reassembling open the valve a few turns before screwing back in. Whole job takes 15min.

The brown plastic taps i suspect may be the same but dismantling them will give you an idea how to proceed. let us know how you get on. Regards Steve

Many thanks. When it cools down, I'll have a go and let you know how I got on. (Of course, I'll have to buy the replacement washers as well!)

Well, I managed to remove the valve units on the kitchen sink taps. The washers seem to be in good condition, but they appear to be fixed in position by a rivet of some kind. Can replacement washers be easily forced over the "rivet head" (for lack of a better term)? I know that on full size taps they are sometimes secured by a nut, but not in this case.
(I also saw that the crystal plastic knobs are split, so am taking the opportunity to reinforce them before they break altogether.)
We visited a caravan service centre this morning, who said that these kind of taps were no longer available, so if the washer replacement doesn't solve the problem, I'll need to buy a new sink as well as a new tap unit!
It appears that I have to remove the vanity unit to access the washroom taps. The unit is now getting rather brittle, so I may need to replace that as well as (possible) replacement taps! It's all getting rather expensive, but inevitable with an older Autosleeper, I think.

Alan, search Eb*y for 1/2" size taps (if thats your size?). Prices seem to vary from £12. New washers would be the cheapest option and they should slip over the top of the rivet, try dipping them in hot water to soften them. As for the brown taps, check the website of the caravan shop in Glasgow. They show your brown plastic taps (Comet Nova mixer tap??) as a complete unit for £21, i'm sure other similar shops will have them as well. Their website shows the taps as having wires for micro switches beneath but might just be a straightforward replacement. Its quite fun doing these type of jobs, you learn so much about your van. Good luck

Alan, yours might even by 3/8" taps, Eb*y shows them complete with new heads from £8. Getting cheaper all the time

Steve - the 3/8" taps look exactly right - and even have new crystal tops! I've ordered a pair for the kitchen.  
I'm still a bit bothered that both sets of taps 'failed' at the same time, in case it is a different cause than washers.
I've ordered a new Cleo Tip-up Basin unit for the washroom and a new set of taps, on the assumption that one or both have failed. Because it's a mixer tap, I can't tell if the water is coming from the hot or cold supply.  We'll see...

Thanks again for the help - I'll update you when everything arrives and I've had a chance to fit them.

There's no such thing as a quick job! The Cleo Tip-up basin unit I ordered arrived OK. Unfortunately, the new design is for surface fitting, not inset. Those with a Topaz will realise that a surface fitting vanity unit means the toilet seat can't stay open (and it would be almost impossible to sit on it!). Fortunately, I was able to cut the fitting to the point it was identical to the old one (phew!), and able to be inset where the original one was.
New tap unit was fitted (micro-switches not required) and everything connected to the water & waste systems. I am pleased to report that, when the system is pressurised, no water comes from the taps unless they are turn on!  Job done.
Final task - fitting a new tap onto the waste water tank (a new post).

Thanks again for all advice given.