This work by the Portuguese composer Bomtempo treats the British national anthem with Classical era variation techniques. It is a stylistically transitional piece showing both late Classical and early Romantic influences.
Attention to clean articulation and precise execution of Classical-style ornaments is essential for this piece.
Comparable difficulty and character — good candidates for what to learn next.
Capriccio and Variations on 'God Save the King' (Op.8) is rated Henle level 6 of 9 — advanced repertoire, roughly ABRSM grades 7–8. In the RCM system it corresponds to about level 7.
You should be comfortable at Henle level 6 — meaning you can already play level 5–6 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
A typical performance of Capriccio and Variations on 'God Save the King' (Op.8) lasts about 8 minutes.
Capriccio and Variations on 'God Save the King' (Op.8) is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.
Pieces at a comparable difficulty and character include An introduction, 5 variations and fantasie by João Domingos Bomtempo, 12 Variations on "Ah vous dirais-je, Maman" by Wolfgang Amadeus Mozart, Italian Concerto in F major by Johann Sebastian Bach — see the full similar-pieces list on this page.