OS Grid to WGS84 lat/long converters are likely to require pure X and Y fields, with values in metres.
Tim has 3 fields - square, easting and northing, containing coordinates to 10 m precision.
UK OS grid coordinates have X values with 6 digits, and Y values with 7 digits (Shetland is > 1000 km N of the Lizard).
Tim will have to add a zero to the end of his easting and northing fields, then get the first digit or two from the 100 km square reference by a lookup table, probably.
The square letters are based on a 5 x 5 matrix, omitting "I", so the first row is ABCDE, the second row is FGHJK etc
The second of the two letters identifies a 100 km square within a 500 km x 500km square, the first letter identifies the 500 km square. The National Grid 0, 0 point is at the SW corner of the "S" 500 km square, and the 500 km square letter will be one of S (SW England & Wales), T (SE England), N (Scotland and England N of Windermere) or H (Shetland and most of Orkney).
There's also a little bit of beach just S of Ravenscar that's in the "O" 500 km square.
Tim's TQ 2803 4395 will have a numeric grid reference of T=(500000E,0N) + Q=(0E, 100000N) + 28030E,43950N, ==> 528030, 143950
The other thing is that conversions frequently aren't all that accurate.
If I put a GPX track into ArcMap at work, the default conversion, based solely on the two geoids and the OS grid projection, comes out something like 110m out (from memory). I've got to select a further "fiddle transformation" to get within a metre or two, and there's a whole list of these fiddle transformations for use in different parts of the country.
The OS page at
https://www.ordnancesurvey.co.uk/business-and-government/help-and-support/navigation-technology/os-net/coordinate-spreadsheet.html contains a conversion spreadsheet and a PDF about coordinate conversions and why you won't get accurate results