Hi Georgie,
you need to explain the importance of a proper stock take, that it is essential in order to get an accurate profit or loss figure. Perhaps tell them that they may end up paying too much tax and certainly will not be able to ascertain a proper contribution towards variable costs and hence not know their break even points. Added to this that it is a requirement and they probably don't want an inspection to uncover any wrong doing!
Ok on a more pragmatic note you need to get them to give you their best estimate in writing. I would tend to look at their purchases in the final month or so of their financial year and see if it makes any sense as they may want to under value the stock. If WIP is an issue they need to give you a figure for that too.
Also, compare the GP margin with last year and see if its comparable. If its massively different, chat with the client and see if that's to be expected.
My Boss is the same, he won't do a stock-take so the accountant just asks for a good guesstimate as Rob states. I tried working it out on opening stock plus looking at sales at 25% profit and seeing if I could come up with a guesstimate, but it was way off what my boss thought it was, so we just went with his guesstimate :)