Did British forces ever bomb/engage Finnish forces after the UK declared war vs. Finland in WW II?

During the declared war between them, no.

However, Britain bombed Finnish territory on the 30th July, 1941, 4 months before their declaration of war on Finland. This was part of OPERATION EF, a raid on Arctic ports by the British carriers Victorious and Furious. Victorious attacked Kirkenes in northern Norway, and Furious Liinahamari (now Liinakhamari) in Petsamo (now in Russia). Liinahamari was Finland's only Arctic port. 11 Albacores (torpedo bombers) and 2 Fulmars (escorting fighters) were lost in the attack on Kirkenes, for one freighter sunk and another damaged (a German naval training ship and other freighters were also attacked, but were missed). The heavy losses were largely due to a returning Ju87 (Stuka) raid escorted by Bf109 and Bf110 fighters; the 12 escorting Fulmars shot down 1 Bf110 for the loss of 2 of their own, but could do little to protect the Albacores, with 11 of 20 shot down by the German fighters. On Albacore shot down a Ju87 which blundered across its path. The raid on Liinahamari was unsuccessful, since the harbour was empty of shipping. The torpedoes were dropped with the wooden jetties as targets, and bombs were ineffectively dropped on oil storage facilities. The raid was intercepted by Bf109s, losing 1 Fulmars (of 5 remaining after 1 had been lost to engine failure before reaching the target) and 1 Albacore (of 9 Albacores and 9 Swordfish). Two aircrews were spotted in liferafts near the coast, but rescue was not attempted due to enemy fighters; both crews died. Overall, the British lost 42 aircrew killed or captured (one tail gunner returning dead), and 3 aircrew (the Albacore shot down on the Liinahamari raid) evaded capture and made it to the Soviet Union.

The high casualties at Kirkenes resulted from the misfortune of meeting the returning German fighters. The scant gains were the result of faulty intelligence provided by the Soviets.