I don´t know if you met a Brit. But it could come from the Cockney Rhyming Slang, in fact this way of speaking has spread to other countries as Australia and others.
So, it´s a combination of words that means one word (concept, idea, etc...)
Well, it´s better by way of an example than with words...so here you are:Nice cup of Rosie Lee
(all that jumble of words means "tea", no more no less...)Dog and bone
- phone.Trouble and Strife
= WifePoppy Red
"Of course my horse
" seems like a corruption (uma corruptela) of that usage, adding some wordplaying to it.