Yes, definitely possible. But this is a DIY group. Why not fit it yourself? You'll get guidance here. You'll save yourself money and you'll give yourself some Brownie points.
I did that. We had this thing called "Harcopak- instant plumbing, just add water" It was in the airing cupboard and consisted of a big angle iron frame with the cylinder below a dividing shelf and the cold water tank with the heating small tank integral with it above. It must have been put into place and then partitioned off, I had to cut it up with an angle grinder to get it out. Anyway, I disconnected everything, left the cylinder where it was, extended the pipes up through the ceiling into the loft, put a large and a small tank on a board supported by steel box sections immediately above the airing cupboard.
It not only improved water pressure to the hot taps, but also hugely increased the space in the airing cupboard so I was able to put some proper shelves in. That kept the Mrs happy. It was a hell of a job mind, first time I'd done any plumbing more than changing a tap washer.
Yes, in fact the OP's situation is much simpler. He's only got to exchange a leaky metal tank with an new poly one. I have to assume that he's got access to his loft big enough to at least get the new tank in.
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