+1
You can pitch onto the cake and make a good beer, but you will be over-pitching. That means the yeast don't reproduce as much as you really want, and a lot of old yeast will be doing the work. A couple of consequences are: 1) You don't get the esters created when the yeast reproduce (actually reproduction only creates the precursers for the esters), so the beer is less complex, and 2) The old yeast might get tired and may not fully attenuate (maybe oly a point or 2 that will not be noticed).
A fermented beer will end up with about 6X what is considered a standard pitch. If you start off with that much, you do not create many new cells.
So to pitch the correct amount, you want to pitch about 1/6th of the final yeast. I generally try to use about a quarter of a cake (I find a pint mason jar is perfect for this - or 16 ozs since you are in the UK). The reason I use a quarter, is because not all the yeast will survive thru the fermentation and it is the best estimate I have seen, and works well.
I'd just pour off about a pint of the slurry, and pitch that in the new beer. No need to wash it. If the jar is sanitized, it can keep in the fridge for a while too. ..... You could get a few beers out of this cake if you work it right.