As the bandwidth resource in TV white space (TVWS) is permitted to be used for the secondary users, multiple secondary networks coexisting in the same geographical area can provide multiple services without interfering with the primary service, such as the TV broadcasting. To satisfy the minimum rate requirements and maximise the sum rate of the multiple services, the problem of resource allocation can be modelled as a mixed integer non-linear programming (MINLP). According to this model, the joint bandwidth and power allocation (JBPA) method is proposed to solve the resource allocation for multiple services. The JBPA method is sub-optimal, which can approximate the performance of the optimal two-step exhaustive search (TSES) method very well, especially when the number of services is larger than the number of idle channels. Compared with TSES, the JBPA method decreases the complexity from exponential level to polynomial level. Besides, compared with one channel occupied by single service, the JBPA can serve more services and provide stable performance when the number of services varies dynamically. Compared with the algorithm random bandwidth allocation, the JBPA can approximate the optimal performance provided by TSES better with the time complexity of the same order.