Yes. Trains always run on every day of the year except Christmas Day & Boxing Day.
Different operators (or even different routes run by the same operator) will have different arrangements but it's likely to be a Saturday service, a Sunday service or a modified weekday service (typically omitting some very early trains).
Remember though that there might be engineering works taking place on that day, meaning that replacement bus services could be in use.
You can check services here:
http://www.nationalrail.co.uk/