Sorry, here is the signature that didn't attach first time, which happens when the text takes a long time to load.

Possibly "H. Adwin", a faint (older?) date of 1869 and a further date of 1918? Although "Hadwin" is a name in the nearby town of Grantham.

I think the signature is H. Ackerman.

The Collection's own entry suggests H [?Adlerman].

This article from 1938 mentions a watercolour artist named Ackerman at a presentation in Lincoln. It’s not much help.

The Lincolnshire Echo article from 1938 is referring, in all probability, to the watercolourist Arthur Gerald Ackermann (1876-1960). Interestingly he was painting in Lincolnshire in 1918 but not, as far as I am aware, at Belton. He did a few oils early in his life but this doesn't look like one of his to me. However, the signature could be read 'Ackermann' as suggested by Andrew Shore.

Except that there is very obviously only one 'n' at the end of the signature on this painting, which excludes Ackermann as a candidate, especially as he usually signed his works as "Gerald Ackermann". Also, there is no capital "H", as can be seen in this signature, at the beginning of either of his first two names of Arthur and Gerald. This work also does not display anything of Ackermann's painting style.

Could it be a German name? There was a POW camp in Belton Park in WWI.

https://www.nationaltrust.org.uk/belton-house/features/belton-park-and-the-first-world-war

"Adlerman" looks possible from the signature but "Adler" would be the more usual form with Adlerman appearing in a few references in the USA.

H. Adler with a date (possibly 17 - 9 - 1918?)