There may be an express term in your contract of employment requiring you to move to another location on request – although the existence of such a clause does not necessarily mean you have to move. Where you have in practice consistently worked may be just as important. Also, a location clause which is drafted very widely (eg "You may be required to work anywhere in the UK") may be unenforceable.
Aside from the contractual position, it may be possible to argue that selecting you to move without making special allowances is indirectly discriminatory. That is, the impact of the move on you, relative to other colleagues, is disproportionately negative for reasons connected to your being part of a group protected by equality legislation. This point has been successfully argued by women who, due to caring responsibilities, were especially badly affected by a move.
Where there is a valid contractual term, refusal to relocate may be a breach of contract. In the absence of a contractual mobility clause, if you choose not to relocate, your job has probably become redundant and you may be able to claim a redundancy payment, subject to you meeting the qualifying conditions (eg two years' service).
A good employer will provide advice and practical assistance to staff, including financial support, to enable the relocation process to go as smoothly as possible. Your employer has a duty to pay reasonable expenses incurred during the course of your employment and this would include reasonable relocation costs.
Your contract of employment may specify exactly what relocation costs your employer will meet.
