Under the regulations forced on the UK by the EU, they are all you can buy.

They are more efficient and save energy.

However, they use more energy to make. They will break down sooner and the replacement parts you will have to buy will have used more energy to make. Plus will cost a lot.

In a dozen or so years they will need replacing. So more costs and a mass more energy used in the making of the new boiler.

But so what, in theory (if not in practice) you are saving the planet.

A combi boiler simply has an inbuilt pump. If the pump develops a fault it will cost double the price of an external pump to replace.

A system boiler (which is what I think your OH is thinking of) also supply’s the hot water to the taps. Great idea, just don’t turn on more than one tap at a time unless you like cool water. To get over this problem, just install a bigger boiler than you would normally expect.

As you have to comply with EU regulations, I suggest you look at http://www.discountedheating.co.uk. Good prices and good service.
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look into the wall hung unit
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its what I do.