Here is what the LMA have - not all survive, though. I had a look at the Times but couldn't see anything on William - Mr Baker, on the other hand, who was the coroner of the 'eastern division of Middlesex' turns up both in mentions of other inquests and also being criticized in 1843 for not being reliable - turning up hours late to inquests. The coroner of the western division, Mr Wakeley, was unwell, though, and Mr Baker seems to have been covering much of his work as well.
It unfortunately looks to me like (from the LMA), that eastern division of Middlesex records have not survived for your dates. You still might be able to find a newspaper record of the event - when exactly did he die, is there a date for the inquest, and what was the cause of death?
