Looks like it's 1x 8 inch cake and 1x 6 inch from the description.
I reckon £15 is about right for ingredients.
3 layers rather than my usual two, so I think it would take 10-11 eggs so £3, and 675g butter, plus probably another 6? oz at least for the buttercream. So call it 4 pats - £8. (£11)
Plus 675g flour, 35p if you use value flour which I find fine. 70p if you have to buy the bag specially. (£11.35)
Sugar about 80p, £1.20 if you have to buy a whole bag specially. (£12.15)
Icing sugar, I think I would need at least 16oz, so probably 1x 500g bag would do it (90p). (£13.05).
Baking powder, negligible if you have it in already, £1.50 if you don't.
Vanilla extract, probably need quite a lot - maybe 4 teaspoons - for something this big which could easily be £1.50 fir even that much if it is decent quality.
A few tablespoons of milk - negligible.
Add a bit of oven time and I think you'd be sitting round the £15-16 mark if you didn't have to buy everything from scratch.
I enjoy baking so I don't think costing my time up for that would be helpful.
My cake would also have only 7 ingredients as opposed to 15:
Flour
Eggs
Sugar X2 types
Butter
Vanilla extract
Baking powder
Milk
Saying that, if I can't be bothered, or have a lot to do in the run up to a party a shop bought cake can be a great option and it sounds like this one is pretty tasty!