What's the UK done to your or anyone else in Europe to make them think that their military is not reliable any more?
UK military commitment to Europe was always via NATO so will not change under Brexit, and the UK still provides the headquarters and much of the troops for the cooperative formations in Europe such as ARC.
UK troops are on the ground in eastern Europe right now in the NATO EFP against Russia, providing I think (couldn't find a source right now) more troops than anyone else is.