Your partner having a Belgian residence permit is not directly relevant.
You may be entitled to bring her with you to the UK under freedom-of-movement rules, but if you're not married that depends on whether you're deemed to have a "durable relationship". Typically several years of shared residence will be expected. If you think you qualify, the way forward is to apply for an EEA family permit in advance.
Hmm, actually it appears that the UK government does not recognize unmarried partners at all under "Surinder Singh" applications (i.e. when the union citizen is a British citizen who has moved to another member state). That is currently being challenged in the ECJ, but the court has yet to rule.
She needs to apply for a standard visitor visa and qualify for it based on her own circumstances.