I'm looking for an equivalent term in English for tsunami. How did people name/describe the phenomenon prior to 1868 -the first time the word was recorded in English according to Etymonline bearing in mind (as stated in the same site) that the word tidal is not a correct synonym?
It was, and sometimes still is, called a tidal wave, even though it has nothing to do with tides.
Tsunami: (it is a unique term in its meaning of big wave caused by a catastrophic event as shown below), the common terms used were tidal wave and seismic sea waves.
Tsunami is a Japanese word with the English translation, "harbor wave." Represented by two characters, the top character, "tsu," means harbor, while the bottom character, "nami," means "wave." In the past, tsunamis were sometimes referred to as "tidal waves" by the general public, and as "seismic sea waves" by the scientific community.
The term "tidal wave" is a misnomer; although a tsunami's impact upon a coastline is dependent upon the tidal level at the time a tsunami strikes, tsunamis are unrelated to the tides. Tides result from the imbalanced, extraterrestrial, gravitational influences of the moon, sun, and planets. The term "seismic sea wave" is also misleading. "Seismic" implies an earthquake-related generation mechanism, but a tsunami can also be caused by a nonseismic event, such as a landslide or meteorite impact.
As above - traditionally, until comparatively recently, a 'tsunami' would have been called a 'tidal wave' in English, dedpite the fact that this term is misleading. The Boxing Day tsunami that devastated SE Asia seemed to be something of a turning point - I can remember TV and radio news in England announcing the catastrophe, and, in some instamces, actually explaining as part of their report that this was a tsunami, and WHY they were using that term instead of 'tidal wave', so although the word may have been recorded in English as far back as 1868, many English speakers were still not using it in daily discourse right up until that point.
This is in fact a much better term for such waves, as they involve a large dropping of the water-level followed by the wave coming in at a much higher than usual water-level, as if a tidal change had happened.
Still, the fact that they have nothing to do with the mechanism behind tides led to tsunami became more popular despite their having nothing to do with harbours.
In Europe, tsunami are rare occurrences. There was no specific term in English, and probably not in any other European Language.
The most well known tsunami to affect Europe is that which destroyed much of Lisbon on 1 Nov. 1755. It is clear from contemporary accounts that there was no specific word to describe the events of that day. Instead more general, or descriptive terms are used: Flood, Disaster, a coming in of the sea, or the sea rushing the land.
To answer the question directly, before the widespread use of "tsunami", people would refer to a flood from the sea following an earthquake.
Prior to the adoption of 'tsunami' (and omitting tidal-wave as stipulated in your question), the phenomenon was known variously as
A seismic disturbance on the sea floor, or experienced at sea. Also: a sudden flood, massive wave, etc., reminiscent of that caused by an earthquake.
1577 R. Holinshed Chron. II. 1039/2 On the Saterday after..chaunced an other earthquake, or as some write, a watershake [margin] waterquake.
or the related and now obsolete, but with early attestation from the same year as water-quake,
† watershake n. Obs. rare = water-quake n.
or, in a noun phrase that seems redundant but that is well attested in the specific sense,
water wave, n.
b. spec. A wave in a large body of water, esp. a sea, caused by a tectonic or geological disturbance such as an earthquake, or by an explosion. Cf. tsunami n.
1851 M. Somerville Physical Geogr. (ed. 3) I. xiii. 270 (note) When an earthquake begins under the ocean, it occasions five distinct series of waves..namely, the earth wave, the water wave, and three other series of waves.
and, finally, the apparently broader yet specifically applied,
sea-quake | seaquake, n.
A convulsion or sudden agitation of the sea from a submarine eruption or earthquake.
1680 C. Ness Compl. Church-hist. 333 This σεισμὸς..is usually understood of an earth-quake, but here 'tis a sea~quake.
1774 O. Goldsmith Hist. Earth I. 121 A violent agitation, or heaving of the sea... This agitation..may be called, for the sake of perspicuity, a sea-quake; and this, also, is produced by volcanoes.
1827 Blackwood's Edinb. Mag. 21 273 The phenomenon called a mare moto or seaquake, ....
'Seismic sea-wave' was in use as early as 1905.
(All block-quoted material from the OED Online.)