tbf though you';re asking installation companies for information that only the manufacturer could be expected to supply. AFAIK this data doesn't exist, which is why no supplier or installer can supply you with it.
the data supplied by steve k though is bit more detailed than most anecdotal evidence, it's just not been carried out under test conditions in a lab or verified externally, and a few bits of data are missing. As I read it he's stated that this warm up time is from cold on first filling the tank, therefore it's pretty much certain that the entire tank was at the temperature of the incoming supply when heating started. It's obviously not 100% accurate, but is likely to be in the right ballpark as long as the tank stat is placed in a sensible location such as the middle of the heating coil at the base of the tank.
I understand the desire for figures, but IMO some of those shouting down this technology are as bad the other way as the snake oil salesmen types in terms of giving the impression that the tech doesn't work at all, which is obviously false. This is a heat pump, as such it is proven technology that has been in operation in other forms for 50 years+, and there is zero reason to think that it won't work, or that a COP of 2.7ish isn't about right for the temperatures given. The technology works, that's not really in doubt (by anyone who understands heat pumps), the valid issue is the lack of accurate data to verify exactly how well it will work in different situations and for different uses, along with a decision from MCS over which category it should fall into for RHI etc (if RHI ever starts anyway) along with miss-selling by rogue marketing companies etc.
I do actually understand the difficulty for the manufacturers in supplying standard heat pump data though, as this is based solely on the air temperature, whereas these devices also collect radiated solar energy, and there currently are no standardised tests designed to measure devices that extract heat from both sources. I suspect that the cop of 2.7 would be the COP without significant radiant heat input from the sun, and that the COP would rise to more like 3.5-4 or higher with the addition of full sunlight giving an extra 1000W/m2 of energy input to the panel.
I really think that MCS are as much to blame here as the manufacturers, as these products have been available in the UK for at least 3-4 years to my knowledge, yet MCS seem to have just ignored them until they suddenly became the next big thing. Simply put, they're guilty of having been asleep at the wheel when they should have been proactively working with the manufacturers to device appropriate test methods and data requirements for these types of products since day 1 of MCS starting up.
That said, I have previously linked on this site to independent test data for one of these products, though the above caveats about it not incorporating solar input in it's figures would apply.