Are there other employees who have the original 10 mile mobility clause in their contracts, who don't want to relocate? If so, how is the company dealing with them?
Whilst you should have read your contract, I think your company should have flagged up changes to the mobility clause and your new extended notice period.
A recruitment consultant told me it will be difficult to get a new job at my level with that sort of notice period.
Does this mean that the jobs you are interested in are not also likely to require a 3 month notice period? Otherwise, you would some understanding/flexibility.
Re references. Do you know your company's policy on providing them? Some clarify minimal details (e.g. dates of employment) and employers have a duty to ensure any information given is fair and truthful. If your employer were to mention leaving without serving full notice, your future employer would presumably fully understand, since you would be leaving early to start a new job with them.
I would suggest contacting your professional body, and getting some advice from them, to ensure your membership isn't jeopardised if you don't serve your full notice.
Overall, I think it's a question of weighing up the pros and cons of leaving early, if a new position depends upon it. And check your contract to see if there is any mention of/likely repercussions from leaving before the end of the notice period.