Clubman is correct, there is no statutory entitlement to disturbance money. However it should also be in your employers best interests to try and encourage as many of their staff to move also.
Firstly you need to look at the whole situation in regards to the new office, are there going to be improved canteen facilites for example, will the working conditions be better? Also you need to get clarification on parking, a lot of new offices have reduced parking in comparison with older ones
I'm in the midst of moving a department 9 miles, however the move will take a lot of staff onto the M50 whereas previously they had no need to do so. Hence their commute will be worse. We're paying mileage at €0.52c per mile to and from work in the first year, half that in the second year and a small bonus, but only to staff who have a longer commute. It's fair in that staff who are discomoded the most, get the most, staff whose commute is shorter, get nothing. Bear in mind, mileage like this is taxable
A lot depends on your employer, their attitude to staff, the ability to replace staff in the new site, the risk they are willing to take if staff leave and how big a row they are willing to get into.
I believe the Labour Court did make some recomedations in the past, ( I heard mention of a case involving Arnotts but not sure if this is correct).
This will result in extra costs for yourself so it is not unreasonable to ask your employer to make some contribution.