Jen, that cage looks lovely, and is obviously great compared to his tiny cage. It's always worth remembering that budgies don't fly up and down and so width is always preferential to height when selecting a cage.
But this is still a lovely cage for your budgie and he'll be very happy in it I'm sure.
BTW, as you're a fellow UK member, Pets at Home do a lot more bird products online than they do instore, so they're good to look at.
ZooPlus is great for cages, cheap perches and bits and pieces.
If you have The Range near you, you can buy natural perches much cheaper in there than Pets at Home (pets at home do lovely java wood perches though).
And The Natural Bird Company make amazing perches toys and things for your little Jake too.