Welcome to our world Jason!
Firstly, it IS indeed a small quickish job when you have the correct kit.
However, and here comes the bad news, your tap doesn't use washers. It uses what is termed a 'cartridge' and there are approx 5000 in use in British taps. The only way to determine exactly which you have is to remove one and do some accurate measurements. It is impossible, genuinely, to tell from the outside. This is why I invented my product.
If you are a competent DIYer then take a nose at our site where you can buy a small kit to do the job. If not, then on our site (under approved installers) you will find a local plumber with a kit to do it for you.
The tap you have, as I'm sad and recognise it, is actually made of reasonably good brass so is worth keeping. Putting new cartridges in will set it back to perfect working order and mean you can keep it for as long as you wish. The alternative is to throw it away and start afresh.
To get a similar quality of brass you'll be looking at approx £200 just for a tap (the kitchen needs something reasonable as it's used more than ALL the rest put together) plus fitting.
