Q.Why My Climbing Hydrangea Does Not Have Peripheral White Flowers
Grown in a pot, has not bloomed for a few years, although it has bloomed previous years (not that many blooms though)

Yes thank you

Consider and rule out to your situation: insufficient nutrients, late frost injury flower bud damage, low soil moisture levels, loss of vigor due to fungal diseases, dense shade. In the extreme southeast of UK, your last date of frost is typically either the last week of March to the second-fourth week of April with variability from year to year. When the flower bud achieves the "broccoli stage", the bud should be green. If you notice any flower bud section that are partially brown, that would suggest a winter or moisture injury and the resulting bloom may be incomplete. If the complete flower bud is brown, it is dead. Diseases like powdery mildew can rob the plant of vigor and reduce bloom size or number of blooms if the infestation is heavy before it is addressed.