The British like to shrink words and let the pronunciation drift around a bit. (We do the same: listen to a Frenchman pronounce “Connecticut.”) And the metamorphoses are unpredictable: you just have to know.
Anyway, here are some examples, often acquired in embarrassing ways!
Abergavenny: Abergnny (hard ‘g’)
Alnwick: Annick
Arbuthnot: A-buth-not
Auchinleck: Afflck (or as spelt)
Beauchamp: Beecham
Beaufort: Bofoot
Beaulieu: Biew-li
Belvoir: Beava
Bethune: Beaton
Blenheim: Blenim
Bolingbroke: Bullingbrook
Borrowes: Burrows
Broughton: Brawton
Buccleuch: Buckloo
Burgh: Bura
Bury: Berry
Caius: Keys (College)
Calverley: Cahvaly
Capell: Cayple
Carnegie: Cahnggie
Cecil: in the family, Sissl
Cirencester: Sista, or Saye-ren-sesta
Clwyd: Cloo-id
Cockburn: Cobun
Colquhoun: Cahoon
Constable: Cunstable
Courthope: Coht-hope
Cowper: Cooper
Cromartie: Crumaty
Cromwell: formerly, Cruml
Dalyell or Dalzell: Dee-l (usually)
Davies: Daviss
De Crespigny: De Crppni
De la Warr: Dlaware
Drogheda: Dry-da
Dysart: Diez’t
Elgin: Elgin (hard g)
Fermor: Fahma
Ffolkes: Foaks
Gifford: Jiffud
Glamis: Glahms
Gower: Gaw
Harewood: Hahwood
Heathcoat or Heathcote: Hethcut
Hepburn: Heb’n
Hertford: Hahfud
Hobart: Hbud
Home: Hume
Inge: Ing
Inveraray: Inveraira
Islay: Eye-la (and on Ilsay, Bruichladdich: Brookladdie)
Kirkcudbright: Kukobri
Knollys: Nowles
Lascelles: Lassells
Legh: Lee
Leinster: Linsta
Leominster: Lemsta
Leveson-Gower: Loosun-Gaw
Leycester: Lesta
MacCorquodale: M’cwkadale
McGillicuddy: Mgillicuddy
McMahon: Mcmhn
Magdalen or Magdalene: Mawdlin
Magrath: Mgraw
Mahon: Mahn or Mahhn
Mainwaring: Mannering
Marjoribanks: Marshbanks
Marlborough: Mawlbra
Menzies: Mingiz (Scotland)
Meyrick: Mrrick
Montgomery or Montgomerie: Mungumri
Moray: Murray
Newburgh: Newbra
Northcote: Nawthcut
Norwich: Norridge
Pytchley: Pie-chley
Renwick: Rennick
Rhys: Rees (usually); Rice (among Anglicized Welshmen)
Romney: Rumney
Roxburghe: Roxbra
Ruthven: Rivven
St. Clair: Sinclair
St. John: Sinjun
St. Leger: Sllinja; sometimes as spelt
Scrymgeour: Scrmjer
Seymour: Seama (or as spelt)
Sherborne: Shbn
Shrewsbury: (locally) Shrowsbry
Sotheby: Suthaby
Southwark: Suthuk
Stanhope: Stannup
Strabolgi: Strabwgie (hard g)
Strachan, Straghan or Strahan: Strawn
Synge: Sing
Tichbourne: Tichbn
Towcaster: Taoster
Trevelyan: Trevillian
Urquhart: Uhkut
Vanbrugh: Vanbra
Wemyss: Weems
Westmorland: Wsmlund
Willoughby de Broke: Willabi de Brook
Woburn: Woobun
Wodehouse: Woodhouse