The number is significantly lower than the 200 to 300 Britons who reportedly fled quarantine in the resort town on Sunday, December 27th.
Valais police said on Wednesday that inspections conducted over the weekend on an estimated 150 Britons who were in quarantine revealed that 12 had left quarantine early.
138 were however found to be complying with quarantine regulations.
On Monday, Swiss media reported that only 12 Britons remained in quarantine of an initial 370 who were forced into isolation after Switzerland imposed a mandatory requirement due to the new mutation of coronavirus which had appeared in the UK.
The quarantine was imposed retrospectively on December 20th, requiring all those who arrived after December 14th to quarantine for ten days.
Many of those who fled quarantine are believed to have returned home or have attempted to continue their holidays in France.
Under Swiss law, anyone who skips quarantine is liable for a fine of up to CHF10,000.