Any will becomes a public document once the executors have been granted probate but that probably doesn't help you because this might take several months. However, your friend could set up a 'standing search' with the Probate Registry. For a fee of just �5, she'll automatically receive a copy of the will (if one exists) as soon as it becomes a public document. (If it takes longer than 6 months, the search has to be renewed with a further fee of �5).
If the relatives of the deceased are trying to hide something, simply telling them that a standing search has been set up might jolt them into disclosing the contents of the will (and putting its provisions into operation).
A more practical step might be to approach the Dogs Trust (which is still better known under its former name of the National Canine Defence League). They're the experts when it comes to caring for and rehoming dogs (even elderly dogs with special dietary needs). They rehome over 10,000 dogs each year. More importantly, they have a policy of never destroying a healthy animal. If your friend could persuade the relatives to let the Dogs Trust take care of Max's future, it might be better than spending months of uncertainty worrying about him:
http://www.dogstrust.org.uk/
(email: fieldinformation@dogstrust.org.uk )
Chris