It may possible to burn modified vegetable oil for heating in place of heating oil (depending on the boiler in question), but it's not really an effective solution, for both financial and environmental reasons. If you currently heat you house with oil you are better off looking at alternatives like a modern wood-fired boiler or perhaps a heat pump.
It's not financially attractive, as biodiesel is likely to cost 70 pence per litre to produce, so if buying commercially it will be more than this. Making your own biodiesel is an involved process and you'll still need to get the raw material. This is not straightforward - waste cooking oil is generally now collected by companies that pay for it and do the relevant paperwork to show that they're dealing with it properly.
Heating oil (kerosene) is only about 30 to 40 pence per litre after the recent fall in price, so you are unlikely to make a financial saving by using biodiesel. You'll also need to invest in some modifications to an oil boiler to make it able to burn a biofuel (for some boilers, especially newer ones, this may not be possible anyway).
Given the cost of biodiesel, investing in a modern boiler able to (or even specifically designed to) burn this fuel will still leave high running costs. Biodiesel has an energy content of about 10 kWh per litre. So even in a modern boiler running at 90% efficiency, the cost per useful kWh of heat will be over 7 pence per kWh (based on the cost above).
By comparison, the cost of wood pellets is about 5 pence per kWh, so an automated pellet system has much lower running costs while still giving the convenience of automated heating. Log fuel will be even cheaper (though more manual work is involved).
Liquid biofuels (like biodiesel or bioethanol) have generally been used for transport purposes in the UK because there was more financial benefit in doing so (due to taxes). However, the amount of biofuel we can produce sustainably in the UK is very small, and can meet only a tiny proportion (less than 5%) of the transport fuel demand - let alone further demand from heating. This applies to both oil from crops like oil seed rape, plus the small amount of waste cooking oil available.
To meet a certain energy demand requires far less land for wood fuel than it would for crops like oil seed rape, as the yield in tonnes of fuel per hectare is much higher for wood. In addition, much less processing is needed to make wood into a useable fuel compared to the processing of oil crops (or indeed the processing of waste cooking oil).
If there is a demand for bio-oils beyond what we can meet in the UK, then much more will be imported, for example from palm oil production overseas with all the environmental damage that is causing - see for example http://www.greenpeace.org.uk/forests/palm-oil.
Considering all these factors, it is much better to think about replacing an oil boiler with a different heating system, rather than replacing the fuel with a bio-oil alternative.