In theory, in an over-simplified building physics model of your home's thermodynamics, yes, all of the wasted energy from inefficient devices goes to providing useful heat to the home, so increasing their efficiency will increase the heating you need from the space-heating system.
But in practice, no, your heating costs will not increase. Not unless you choose to turn up your heating.
At least, in general, that's how it goes.
The thing is, that incandescent lights tend to add heat to places where it's not particularly useful: the centre of the ceiling of a room.
For a combination of reasons, that's rarely useful heat.
Particularly in older UK housing stock, rooms have high ceilings with thermal stratification, which means a layer of warm air stays stuck at the top of the room. Tha layer is higher than thermostats and radiatior TRVs, so changing its temperature won't change the behaviour of the automatic heating controls.
What will happen is that the void between floors, or the loft, will get very slightly warmer. The void between floors is typically ventilated to the outside with air bricks, so your incandescent lights will warm up the outside air slightly.
The temperature field in most rooms in UK housing is pretty steep, with floors being a few Kelvin cooler than ceilings. The bigger the difference between the temperature at your feet and at your head, the less comfortable you are. The heat from lighting tends to make that temperature difference bigger, thus decreasing your thermal comfort.
and although you referred to peak summer weeks, I'm guessing your heating is turned off for a lot more of the year than that: May to September or so would be fairly typical in the UK.
To bear the theory out, see Brunner et al, who looked at heating bills in dwellings which had incandescent light bulbs, and those that had more efficient compact fluorescents (CFL). They found no support for the hypothesis that CFLs cause increased heating costs.