It might be better to tackle the problem a different way. The pension provider (and anyone else who has control over your late uncle's estate, such as his bank) are obliged to pay out in accordance with the rules on intestacy. They have no choice in the matter. However someone who has been financially dependent upon a deceased person can apply to a court for an order
varying the rules of intestacy, under the Inheritance (Provision for Family and Dependants) Act 1975. A court should be satisfied that you were financially dependent upon your uncle simply through you swearing an affidavit to that effect. Once you have a court order stating that you should benefit from your uncle's estate, the pension provider (and, say, his bank) will be obliged to ensure that you get something.
[Note: I've simplified that a bit. There is actually a requirement for someone to seek a 'grant of representation', in the form of 'letters of administration', allowing them to distribute your uncle's will in accordance with the intestacy rules or, if your application for a court order is successful, in accordance with the provisions of that order].
So, as Sapelesam suggests, you're going to need the services of a solicitor.
{A further note, which has just crossed my mind: In order to convince a court that you were financially dependent upon your uncle, you would need to show that such a financial dependence applied immediately prior to his death. e.g. if you're a university student and you were being funded through your studies by your uncle. Showing that you used to be financially dependent upon him, although you're not now, wouldn't be good enough. However you could still seek to convince the court that your uncle stood in the role of a parent and treated you as his own child. Then, even if there was no financial dependence immediately prior to your uncle's death, you can still ask the court to vary the inheritance rules in your favour]
http://www.legislation.gov.uk/ukpga/1975/63