Berkeley (Castle): barkly. Absolutely not 'burkly'
Caernarfon: the English pronunciation is 'kuh-nar-vun', with emphasis on the 'nar'; the Welsh pronunciation is a bit different.
Arundel: ah-run-dul, with the stress on the A at the beginning.
Reading: redding, not as in 'reading a book'
Norfolk/Suffolk: the names end with an 'uck' sound, not 'ohk' as in the word 'folk'
Scarborough: scar-buh-ruh or scar-bruh
Marlborough: marl-buh-ruh or marl-bruh
Windsor: win-zer or wind-zer
Rievaulx (Abbey): ree-voh
Jervaulx (Abbey): jair-voh (I think! Someone please correct me on this if not)
Beaulieu (Abbey): byoo-ly
Tewkesbury: chooks-bree or chooks-buh-ree (with a long oo as in 'woo', not as in 'book')
(River) Thames: temz
Thame (town in Oxfordshire): tame
Loughborough: luff-buh-ruh or luff-bruh, emphasis on the 'luff'
Carlisle, or the name Lisle: ly-ul, with a silent S and a long I.
Southampton: pronounced as though it's spelt with two H's: south-hamp-ton. Northampton, however, isn't: north-amp-ton. (Though actually a lot of English people drop their H's and pronounce Southampton as something like 'sarf-am-ton', but let's not get into that discussion.)
Royal Leamington Spa: the second element is 'lemming-ton' not 'leeming-ton'
Knaresborough: nairs-buh-ruh or nairs-bruh, emphasis on the first syllable.
High Wycombe: wiccum
Shrewsbury: nowadays mostly pronounced as it's spelt, though you still sometimes hear people pronouncing the first syllable as 'shroze' not 'shrooz'.
Salisbury: solz-bree or solz-buh-ree
Southwark: suthuk ('th' as in 'the')
Birmingham/Nottingham/Eltham/Hexham/Cheltenham etc: the last syllable is pronounced 'um', not 'ham' like the meat. Nottingham when spoken fast by some English people comes out something not far off 'no-ih-num', with the T replaced by a glottal stop. Cheltenham is often pronounced 'chelt-num'.
Westminster: pronounced with the emphasis on 'west', not on 'min' as I've sometimes heard people say it.
Cinque Ports: sink ports, i.e. with an anglicised pronunciation.
Tintagel: the G is soft as in 'gin' or 'jelly', and it's emphasised on the second syllable, i.e. TinTAJul.
Belvoir (Castle): beaver
Ely: like 'freely' without the 'fr', emphasised on the first syllable, not like the names Eli or Ellie.
Alnwick: annick (yes, the L and W are both silent)
Cirencester: siren-sester (i.e. one of the few names ending in -cester which is pronounced as spelt)
Manchester/Lancaster: pronounced as spelt
Slough: rhymes with cow
But, Brough: bruff, as is Burgh-by-Sands, where Edward I died in 1307
Cambridge: first syllable is pronounced 'came' not 'cam'
Lewes: like the name Lewis, not 'looz'
Savernake (a forest in Wiltshire): savver-nack
Ouse (a river in Yorkshire): ooze
Cherwell ( a tributary of the River Thames): char-well
Caerphilly: car-filli, emphasis on the 'fil' (English pronunciation)
Edinburgh: edin-bruh or edin-buh-ruh
Dumfries: the second syllable is pronounced 'freess', i.e. with a soft S sound, not like the words 'fries' or 'freeze'
Magdalen College, Oxford/Magdalene College, Cambridge: maudlin
Gonville and Caius College, Cambridge: Caius is pronounced 'keys'
Despenser: duh-spenser, emphasis on the 'spen'
Interesting facts: Lincoln in fourteenth-century documents was called Nicole, York was Everwyk, and Stirling was Strivelyn. Warwick was spelt Warrewyk or similar.