You can improve the insulation and draughtproofing, and that will make the house noticeably warmer. You may be able to get a free or subsidised work, start by looking on the BG website.
An old system is likely to have a lot of sediment and corrosion, and you will do nothing but good by giving it at least a chemical clean and fitting a system filter. The clean is a cheap and easy DIY job but you will need a plumber to fit a filter (it does not need a gas engineer).
There is a risk that your old boiler might have been neglected and break down needing a part that is difficult to come by, or it may soldier on for years. Try to get a recommendation for a local independent engineer to service it.
If you are moving in this winter, look for plastic glazing film that you can tape over windows as temporary double glazing. It is not elegant but makes a quick improvement.
Try not to drape wet washing inside the house as it will cause damp and mildew.
Electric heating is much more expensive to run than gas, but would get you through a cold spell. An older house probably has a hot water cylinder with an electric immersion heater that you can use when the boiler breaks down. Fit two red insulating jackets round it, and foam lagging on all pipes. An experienced old plumber can easily swap a faulty immersion heater. If it is old it needs some skill to take out the old one without damaging the cylinder.