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Is it not possible to get copies from the Land Registry? I think I may want to do this.
You can get copies of whatever documents the Land Registry have on file. To be honest, it's probably not really necessary - while the Land Registry's document retention hasn't been that great in the past, I'd trust them to be able to hang onto any documents they already have. The benefit of having the old title deeds is to fill in the gaps in the Land Registry's documents.
Check with the conveyancing solicitors who acted for you when you bought the property. If they don't have them, then there's probably not a lot else you can do.