I've just spotted that you added additional information (i.e. that your father paid for the headstone) while I've been typing. I'll post anyway (in 2 parts because of AB's limits) and then add a further bit at the end.
Let's start by assuming that:
(a) your father left a valid will ; and
(b) that his carer was named as executor in that will.
If so, the carer should have sought grant of probate. Once probate is granted any will becomes a public document. To obtain a copy of the grant (together with the will), see here:
http://www.hmcourts-s...e.gov.uk/cms/1226.htm
Your father's will defines how his executor must deal with his estate. If he left everything (or just his personal possessions) to her, she's perfectly entitled to retain things like photographs.
If your father died intestate (i.e. without a valid will) you need to apply for 'letters of administration' which will give you control over his estate, which you must distribute in accordance with the intestacy rules. (The Probate Registry can advise you). The carer will have no entitlement to hold or control any part of your father's estate (including things like photographs).
The only exception to what I've written above is that if your father's estate was valued at less than £5000 there is no need for anyone to apply for a grant of representation. You can distribute the estate (in accordance with the intestacy rules) without any formalities. (Again, the carer would have no right to any part of that estate).