Below is a listing of the first known reference in newspapers to cricket being played by teams starting with the letter H in various settlements in Wales during the 19th century.
Hafod 1860
Hafod Star 1876
Hafodybwch 1870
Hakin 1891
Halcyon 1869
Halkyn 1895
Halton 1869
Hanbury (Pontypool) 1870
Hanmer and Gredington 1863
Harlech 1877
Harlech Visitors 1899
Haverfordwest 1835

Credit – Glamorgan Cricket Archives.
Haverfordwest Apprentices 1882
Haverfordwest Commerce House 1866
Haverfordwest Early Closing 1866
Haverfordwest Grammar School 1860
Haverfordwest Juniors 1859
Haverfordwest Juveniles 1862
Haverfordwest Printers 1849
Haverfordwest Rifle Corps 1860
Haverfordwest Schools 1849
Haverfordwest United 1861
Haverfordwest Volunteers 1864
Haverfordwest Young Beginners 1867
Hawarden 1857
Hawarden Castle 1868
Hawarden Grammar School 1868
Hawarden Gymnasium 1890
Hawarden Park 1857
Hay-on-Wye 1834
Hean Castle (Mr. Vickerman’s XI) 1873
Hendy 1896
Hengoed (Ruthin) 1868
Herbrandston 1859
Hereford, Newport and Abergavenny Railway 1857
Hick’s Shoe Factory (Nantyglo) 1876
Highmead House (Lampeter) 1891
Highmead Park 1897
Highmead Wanderers 1874
Hill Street Juveniles (Rhymney) 1871
Hirwaun 1867
Holton 1893
Holyhead 1852
Holyhead Amateurs 1899
Holyhead Boys 1863
Holyhead Intermediate School 1899
Holyhead Ladies 1899
Holyhead Visitors 1899
Holywell 1796 (1843)
Hope (Holywell) 1880
Houghton 1896