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In the past decade, the technology industry has adopted online randomized controlled experiments (a.k.a. A/B testing) to guide product development and make business decisions. In practice, A/B tests are often implemented with increasing treatment allocation: the new treatment is gradually released to an increasing number of units through a sequence of randomized experiments. In scenarios such as experimenting in a social network setting or in a bipartite online marketplace, interference among units may exist, which can harm the validity of simple inference procedures. In this work, we introduce a widely applicable procedure to test for interference in A/B testing with increasing allocation. Our procedure can be implemented on top of an existing A/B testing platform with a separate flow and does not require a priori a specific interference mechanism. In particular, we introduce two permutation tests that are valid under different assumptions. Firstly, we introduce a general statistical test for interference requiring no additional assumption. Secondly, we introduce a testing procedure that is valid under a time fixed effect assumption. The testing procedure is of very low computational complexity, it is powerful, and it formalizes a heuristic algorithm implemented already in industry. We demonstrate the performance of the proposed testing procedure through simulations on synthetic data. Finally, we discuss one application at LinkedIn, where a screening step is implemented to detect potential interference in all their marketplace experiments with the proposed methods in the paper.