A really good bit of sleuthing there, congratulations on finding this. For posterity I'm going to append the PPS5, which was a statutory part of the planning process for historic buildings (now GPA, Good Practice Advice).

To summarize, the building was originally put up by a builder, Henry Staines, in 1877, who lived in one (northern) part of the current hotel, so number 63 Great Eastern Street, with the rest of the building (no. 61) used as a warehouse / showroom for cabinet makers, originally Mr. Richards and John Boswell, then Hart and Co by 1895. This would have been a fairly crude and dusty affair, with stock piled up high in large rooms with high ceilings, and a constant in-and-out of stock all day long.

A fine art publisher and framer (Lee Brothers) took the No. 63 site over in 1899 until 1918. There was a fire there in 1923. It was then used by a furniture company in the 1930s. From approximately 1940 to 1970 the building was used by Natelys Ltd, a rope and twine manufacturer, the longest occupant. The last trader at No. 63 was Salins Ltd, an upholstery business who operated from the warehouse from about 1970 to around 1976. My suspicion is they stopped operations after a fire and the building was derelict from that point onwards. Salins Ltd was struck off the Companies House register in 1980. The site has been unused for a very long period of time - over 25 years - until that report was issued in 2012. I vaguely recall the area from the 1980s and it was derelict then.

No 61, which is now the restaurant side of the building, was a cutlery wholesaler, Priestly and Moore, when that part of the building was known as Valiant House. They traded there from 1980 until the mid 1990s. Priestly and Moore were a well known cutlery maker in Rockingham Street, Sheffield and Valiant Plate was one of their trademarked brands. They closed in 2016. My guess is that Valiant House was their London base. From time to time eBay and related sites sell Priestly and Moore silverware -at least some of which would have passed through the building.

Very little of the original structure has survived into the current hotel, it is essentially a new build, but one designed the complement the original design and the overall look of the area.

The Griffin Pub, on the other hand has been retained and refurbished as part of the development and is the more important feature, historically.

This is what the building looked like in 2008 (and it would have looked similar to this in 1877). No. 63 is on the left. At this point both buildings had been unoccupied for many years. If you then compare it to the picture right at the top of post 1, you will see how this all fits in. I'm sure the developers are pleased with how this worked out.