The particle -kke is an interrogatory particle that marks a recollection, or the failure thereof, in the case a question word appears. The particle's usage is often introspective: the speaker asks him/herself whether something is recollected properly.
Recollections are usually about the past, but it is possible to ask oneself whether a certain event in the future, or a state that ranges from the past into the present, is properly recalled. In that case, many languages use past tense to mark the non-past event.
The particle -kke often appears with -da, or its past form -dat-ta, as in the OP's example eigo-dat-ta-kke. In the form -dat-ta-kke, past tense -dat-ta emphasizes the function of introspective speech marked by -kke. Translations into English can then use the past tense, and possibly the adverb again:
'What was (that) again?'
The OP's example must be understood in one specific way. The example is repeated below:
'Was it English from the first period today?'
Since the example contains 今日 きょう, rather than 今朝 けさ, we can infer that the speaker asks before class. S/He is trying to recollect whether English is the first subject of the day. In that case, the speaker tries to recollect (remembered) data of a future event. Even though the event is about the future, the past tense -dat-ta serves to emphasizes the introspective function of -kke. The English translation shows that using the past tense in these situations is not unique to Japanese.