I can see the more "efficient argument" in terms of replacing these old boilers, but the maths does not always add up.
As someone pointed out, these systems are gravity fed. As far as I know replacing with a modern boiler would require a pressurized system. Depending on how good the pipework is, you may end up with leaks due to the new pressure. The costs could soon mount up to bring an aged system up to standard. We were quoted upwards of £3000+ (two quotes) when British Gas tried to condemn the boiler (just before winter...nothing like a bit of seasonal pressure to make a sale).
So, new system..costing £3000...maybe saving £300 a year would take you 10 years to get it back. What is the chance of it not breaking down or even lasting 10 years with all the electronics in even the simplest of new boilers....not very good.
Furthermore, I would take a guess that many people would not be recommended to retrofit in a heat only boiler or to choose the simplest solution. In most situations people are encouraged to fit a combi boiler of some sort either due to what people think is best or just sales pressure. That just increases the installation costs further...
Furthermore, we have the side issue of material waste. How good is that for the environment. The fact these appliances last half the time (if that) before needing to be replaced.
So what is the true efficiency saving...it is hard to say. If you are planning a major renovation then of course replacing the system makes perfect sense (this is what I plan to do). But if it is working fine, and you operate it as efficiently as you can (good controls and insulated tank) then I say stick with it until fails. Even than as someone pointed out, there may not be new parts but there are still plenty of used spares floating around....
So many household appliances that were once designed for lifetime use are now becoming consumables. UPVC windows are the worst offenders. Marketed as lifetime products that do not need to be maintained, bah, they have barely made their money back in savings before they are replaced again.
Sorry to give the impression that I do not care about saving energy nor efficiency. This is not the case, I try to be as efficient as possible. But quite often people are sold a sales pitch, not the facts....