 Nyorai kupfuurira kweiyi ndima - Boyce akatambira chikwata chebhora chevakomana vechikoro cheEngland uye chevakomana vechikoro cheEssex mukiriketi. Akabatana neWest Ham semudzidzi muna 1959 uye akaita chikwata chake chekutanga mumutambo weSouthern Floodlight Cup uchirwisa Millwall musi wa13 Gumiguru 1959. Mutambo wake wekutanga weFootball League waive pamusoro pegore gare gare, musi wa22 Gumiguru 1960, mukukunda 5-2 kumba vachipesana nePreston North End. Akaita 342 kuoneka kweWest Ham mumakwikwi ose, achiwana 29 zvinangwa. Izvi zvaisanganisira 282 makwikwi pakati pa1960 na1972, umo akawana zvibodzwa makumi maviri nezviviri. Akaitawo 22 FA Cup kuonekwa achiwana zvibodzwa zvishanu, chakakosha chaive mukukunda mu3 × 2 kukunda Preston North End mu1964 FA Cup Final. Akanga ariwo nhengo ye1965 European Cup Winners Cup yekukunda timu musi wa19 Chivabvu 1965. Zita rake remadunhurirwa rokuti, Ticker, rine chokuita nebasa rake sokurova kwomwoyo kwokukunda ikoko mukombe. Mwaka wake wekupedzisira maviri nekirabhu, 1971-1972 uye 1972-1973, akaona Boyce akaganhurirwa kune matatu ekuchinja maitiro sezvo aishandiswa se backup yaTrevor Brooking, Billy Bonds naPat Holland. Akapihwa mutambo weuchapupu uchipesana neManchester United, inotungamirwa neyaimbova mutambi weHammers Frank OFarrell, musi wa13 Mbudzi 1972. Kuonekwa kwake kwekupedzisira kweWest Ham kwakauya musi wa30 Zvita 1972 mukukundwa 2-1 kure neLeicester City. 