The good news is, Victoria British Sells them (or a reasonable facisimi) I asked them about it when I called on a different issue. The bad new is, they want $129.95!!!
However, (and I'm not a Healey expert so don't hold me to this, but...) In many cases, these old British relays are in cans and use "contacts" that often get dirty or gummy. Usually you can gently pry apart the can from its base and examine/clean the contacts and also look for any poor connections from the contacs or coil to the connectors. You can clean the contacts with a strip of light emory paper and also get some electrial contact cleaner from Radio Shack. The connectors on the base can be cleaned nicely with a pencil erasor and you should examine the connectors on the wires. If they are badly corroded, you should replace them. Just something to try before you submit to buying a new relay (you may have already done all this).
Hope this helps,
George
PS: If VB sells them, other places probably do also, so I'd call around for prices first.