This is unfortunate and sole destroying! The fact that it costs £5 a day, particularly for a two-bedroom unit, is simply unacceptable. Unfortunately, this is a reality in the UK and many other regions around the world.

I'm unsure if this is a solution, and I haven't personally experienced it myself, but have you ever thought about trying infrared heating?

The reason for mentioning them is because I have had to do some research on them and from what I found, they can be up to 30% more energy-efficient than traditional convection heaters. Essentially, this could potentially lead to a reduction in your electrical bill.

In fact, despite this being an American study, the American Society of Heating, Refrigerating and Air-Conditioning Engineers published an article back in 2007 stating that infrared heaters consume about half the energy than unit heaters.
Source: https://www.reverberray.com/wp-content/uploads/2013/01/emerging_tech_small.pdf

However, the next question arises: Are they effective at heating, and how do they stack up against convection heaters?

Once more, my understanding is based on the data I've encountered, but traditional heaters will heat up the surrounding air (which takes up a lot of energy). Once the air is heated, you can switch off the heater and the room will remain somewhat warm for a while longer. However according to this article https://laminaheat.com/en/infrared-heating-panels/ because infrared heaters don't rely heavily on heating the air, they can help reduce humidity levels in a room, which might help with the damp you have.
Many describe infrared heating, in the same way the sun keeps you warm on a cold day, you can feel comfortable even though the ambient temperature is chilly. However, what many don't say is, what happens when a cloud covers the sun?... it goes instantly cold!

Another concern I've heard people mention is that with infrared heating, individuals may feel warmth on one side of their body while the other side remains cold, as the infrared heats whatever is in its path. In contrast, when the air itself is heated, warmth tends to envelop individuals more evenly.

All of the above considerations might make it seem like using infrared heating is a lost cause. However, I believe its effectiveness will vary depending on the circumstances. Like what you've described, I used to live in a home in the north (UK), and houses there aren't always well-built.
The house was always cold and even with gas central heating, it would have to work really hard to even get the house to 16°C. It felt like a never ending battle with all the heat escaping into the atmosphere (it is only effective if you can trap that heat into the room / home).
For us, because we were in a big home, it was unlikely infrared heaters alone would have sufficed, but for a smaller 2 bedroom unit, maybe under those conditions, infrared becomes just as affective, while benefiting from the reduced energy bills!?

There are also advantages to using infrared heating, so it's not all negative.

For example, convector heaters can dry out the air, whereas from my understanding, this does not happen with infrared heating. Additionally, infrared heaters are renowned for their remarkable lifespans with minimal required maintenance, attributed to their lack of moving parts. Furthermore, because there is no convection, there is better air quality and no movement of dust particles in the air, which is beneficial for those with allergies.

Furthermore, based on other sources I've read, infrared heating is considered an effective method for preventing damp from forming. This is because the infrared wavelengths are absorbed into the thermal mass of the walls, gradually spreading warmth through the brick, mortar, and plaster, ultimately heating up any dampness present. So, perhaps it could assist with this aspect you are currently dealing with?

Moreover, because they don’t rely heavily on heating the air, infrared panels can help reduce humidity levels in a room. This can be beneficial in damp or poorly ventilated spaces where moisture accumulation may cause issues like mould growth or discomfort.