We show that the problem can be solved in plain-exponential time if H has cliquewidth at most k. Given a k-expression for H, we can count the number of graph homomorphisms in time O((2k+1)^n(G)), and to complete the result, we show that if H has cliquewidth at most k, then a k-expression for H can be found in time O((2k+1)^n(H)).
Since complete graphs have cliquewidth 2, and bounded treewidth implies bounded cliquewidth, this unifies and extends the previously known plain-exponential time cases.