You can each purchase a share in your parents house which equates to the amount of money you put in. So if the house is worth say 200,000 and you put in 20,000 each you each get one tenth. Stamp duty is charged on the money passing, under 127,000 is exempt. It is simplest if you raise the money elsewhere than on your parents property but some lenders will allow mortgages in these types of situation, assessing just the childrens income but with the parents also being a party to the mortgage. You can also buy additional portions over time if your parents need more money and you can afford to give it to them. The only cost is legal fees (shouldn't be too much) and land registry fees.
You should make an appointment with a solicitor to go through your options, if your parents gift you the house and then you raise a mortgage they will need independant advice (addidtional cost and they loose control of their asset). If they sell you portions of the property for full market value one solicitor will be enough and they retain most of their property