There isn't a simple answer to a question like that, there are so many variables.
First off, how much is a new gas supply going to cost ? ... and therefore how much money are you going to have to save to pay for it ? ... and how long are you prepared to take to get a payback ?
It's not as simple as lecky costs x p/kWh and gas costs y p/kWh, therefore you need to use (gas pipe cost)*100/(x - y) kWh of energy to get payback. You also have to take into account differences in installation costs for the system, and of course you also need to consider what's already installed.
First off, if it's a 'greenfield install' (ie there's no existing installation to consider), then my
personal preference would be a thermal store or heat bank. Your "electric boiler" in this case would simply be a suitable size/quantity of immersion heaters and their associated supplies. In that case, you've completely eliminated the cost of the gas boiler install against (in most cases) some fairly basic electrical installation. It may also be practical to go on an "Economy 7" type tariff and reduce the difference between gas and electric prices.
As you'll know if you browse this and other forums, to say that not everyone is a fan of thermal stores or heat banks would be an understatement
So if you aren't going that route, then a standard open-vented hot water cylinder will do your hot water (again with immersion heaters) - or an unvented (pressurised) cylinder if you want "mains pressure" hot water. That leaves you with the heating.
When I was researching option before fitting the thermal store in the flat, I found that there are a few electric boilers on the market, but IMO they were very expensive for what they are - effectively a heater element inside a bit of water pipe, with some insulation, a case, and controls. If you wanted wet central heating then you 'd need to use an electric boiler, or a cylinder you can connect it to (ie a thermal store or heat bank).
Again, with a blank sheet, you could avoid wet heating. Some people go for storage heaters, but IMO these are really, really dire and need you to guess in advance how much heat you will need the next day - and lack controllability. We have them in the office, and often have to open windows to let heat out ! Or there is underfloor electric which is relatively cheap and easy to install, but got a bad reputation years ago due to the tendency to use off-peak for heating and thus try to use the concrete floor as an uncontrolled storage heater.
Other factors that may influence you might include the availability of locations for gas flue and condensate drain (a factor leading me to investigate electric heating for the flat). And having determined possible locations for the boiler, how easy (or otherwise) it is to get the appropriate plumbing to where it's needed.