A bit tangential, but 'Leicester' is one of those wonderful British place-names that doesn't really follow any English pronunciation rules and you just have to know the right one...
All of the recent fuss about Welsh placenames only serves to highlight that places in England, in contrast, are usually named in languages that no-one speaks any more. At least Welsh is still spoken.
Latin gives us, via Old English, the "-cester" in all of the placenames mentioned elsethread, as well as "-chester" and "-caster". Old English gives us all of the "ton"s, "hamp"s, and whatnot. The "win-" in "Winchester" is Celtic, as are the "dor-" in "Dorchester" and the "man-" in "Manchester". The "lei-" in "Leicester" means an unploughed meadow, a.k.a. a lay or lea.
When one isn't a native Latin or Old English or Celtic speaker and cannot even understand placenames in England, it does seem a little silly, and missing a huge elephant in the room, to be worrying about Welsh placenames. (-:
This is why the names don't follow Modern English pronunciation rules. They aren't actually Modern English.
I was born in England, but we emigrated to Canada when I was 5. A few years later, we returned for a visit. My mother and I were on the Tube when I announced loudly `Ooh look, Mummy, the next stop is Lye-ces-ter Square!'. She shushed me and said she didn't want the other passengers to think we were Canadians.
We've got a Leicester here in Massachusetts which is also pronounced 'Lester'. It is just West of Worcester, which is pronounced 'Wuster'. But they become 'Lestah' and 'Wustah' with a Boston accent.
In this case 'Leicester' is pronounced 'Lester'.