Any reason I could not connect my central heating controller and pump through one of these as a back-up against power cuts?
No problem at all really. The easiest way to do it is to arrange for the supply to the whole system to be via a 13A plug which normally goes into a socket on the wall. In many cases, it will simply be a matter of replacing the fused spur with a single socket, and putting a plug on the end of the flex that went into the fused spur. Once you have that, it's simply a matter of unplugging the system, plugging in the UPS to the wall, and plugging the system into the back of the UPS (you may have to remove the 13A plug and fit a CEE22 plug (aka 'kettle plug')).
As knighty says, you need to look at the runtime of the UPS with your system load. I'd suggest the easiest way to do this is to get the supply altered first, then you can use one of those plug in energy monitors to see how much power your system takes to run (don't forget that it will take different amounts of power depending on what's running - pump, boiler with burner lit, etc). Measure both "power" in watts, and "volt amps" (aka reactive power in the trade) and get maximum values for both.
The first critical thing is that any UPS you get must have a capacity which exceeds the two values you've measured - they normally have two ratings, power and VA, although they might not both be shown in the description. If the UPS is not large enough then it may well shut down when the load gets too high.
Then you can look at runtime. Most UPS manufacturers have some sort of runtime chart or calculator for their products - so you can select a product, and work out the runtime available for your load. You may have to do some guestimation since the load won't be constant.
To get more runtime on smaller UPS systems, it's usually easiest to buy a bigger unit. Alternatively, and this isn't supported by the manufacturers on most small units, you can add extra batteries - this may mean modifying the unit. If you decide to do this, start with an oversized unit because ... the smaller units won't be continuously rated ! When mains is present they are doing very little, but when the mains goes off you will be running the inverter which will create heat, and when the mains comes back there will be heat from the charging system. On small units they will tend to rely on the battery giving up before the inverter gets too hot - so adding batteries risks overheating. If you start with an oversized unit, then this shouldn't be a problem.
I still wouldn't suggest adding batteries hugely bigger than the originals - eg if the original battery was only 7Ah, I wouldn't suggest connecting batteries of tens of Ah (such as an 110Ah leisure battery) as this may overwhelm the charger when the mains comes back on.
Take take this as anything scientific, but my "gut feeling" is that something like a 1000VA unit should be fine with extra batteries to run (say) a 200W load. Something like the APC unit someone mentioned earlier has (IIRC) something like 24V 7Ah or 11Ah batteries. Adding some extra capacity up to (say) 40 to 50Ah total shouldn't be a problem.
This isn't something I've tried, it's just my "gut feeling" about where I'd be starting if I were to experiment.
I've changed batteries in a few of these small units from time to time at work. Occasionally we end up with "surplus" ones when it's been a better choice to simply fit a new unit, and a couple of these surplus ones now run my computers at home

However I'm still waiting for the boss to make a decision about our big UPS at work (about 8kVA running off that) - that takes 20off 44Ah AGM batteries. About a 1/4 ton and the replacement cost is over a grand

The last set dried out and are knackered though some of them might be usable to for lighter duties with the addition of a touch of water.