The big name in that field, without a doubt, is Dreweatts and Bloomsbury Auctions:
http://www.dreweatts.com/cms/pages/model-engineering-toys-and-collectors-items
as exemplified by these news items
http://www.bbc.co.uk/news/uk-england-coventry-warwickshire-32331602
and
https://www.collectors-club-of-great-britain.co.uk/model-railways/news/dreweatts-to-auction-the-dennis-brown-collection-of-gauge-1
However they only have sales twice per year and there's nothing scheduled on their calendar during the first three months of the year. (My links above refer to sales in April and September so, if they were part of a regular pattern, the next such sale would be in April).
Otherwise (if you're selling) you'd probably need to search out a general auction house which might be 'on the radar' of people interested in model engineering, such as those that have specialist sales of items such as die-cast toys (where model engineering items might fit easily alongside). One of the best known of such auction houses is down the road from me:
http://www.lskauctioncentre.co.uk/
To the best of my knowledge, there are no such specialist auction rooms in Lincolnshire although, of course, the county is home to a major dealer for buying and selling model steam locomotives, etc:
http://www.stationroadsteam.co.uk/
Perhaps someone at LDMES might be able to help you?
http://www.lincolnmes.co.uk/