I'd send an email to the Hilton and ask them for a quote from a local 'mini cab' firm. It should be in their interests to find somewhere reasonably priced because if it's too expensive your best option would be to find a hotel near Heathrow for the night.

From the top of my head, as a guesstimate totally devoid of any factual basis, I would expect a minicab ride to Heathrow to cost between 40 & 50GBP from the Docklands. A Black metred Taxi might be higher.

EDIT to add: This is explained much better by ajax in post #6