I tried the first set of code.

UPDATE [dbo].[1870_1880_DAT]

SET [TOWN] = rtrim(ltrim([TOWN]))

WHERE [TOWN] <> rtrim(ltrim([TOWN]))

The query ran with out errors.

I tested the query's output by using a SELECT DISTINCT query. The output wasn't ordered sequentially in ascending order. I have only see this kind of output because I had a space in front of the text in the field of a record.