Technically, because this pertains to waste generated by a business activity (renting a property), it's hazardous waste unless fully decontaminated (which itself would also generate hazardous waste) and needs to be taken to a licensed disposal site.
If it was you changing your own oil tank at your residence it would fall under the purview of domestic waste, which is exempt from most requirements, and the "Waste Collection Authority" (usually the district or county council) is legally compelled to take it away if you chop it up and put it in the bin, hazardous or not.
The stuff comes out of the ground in the first place, so just putting it back.
This is light heating oil, so I would use old sawdust to absorb the leftover rubbish in the tank, then burn it at high temperature. That's what was going to happen to the oil anyway. Then I would cut up the plastic tank and put it into the recycling bin to be processed.
At our local recycling centre, if it was old engine oil, you empty the oil into a big collection tank, then you are told to chuck the empty container into landfill. That's pretty common. There is not a good solution for contaminated containers.
I'm sure there are professional companies which will come and clean out an old heating tank and deal with the contaminant. That will cost a fortune!. I would be wary of letting a plumber clean it for £35. Probably Fairy Liquid and hot water to emulsify it, then down your drain!. They would need to be licensed to dispose of the waste correctly.
From a practical point of view, this is probably the most sensible approach, it would still technically be illegal to burn the oily sawdust, but it's unlikely to cause environmental harm if done with reasonable care.
If OP wanted to completely cover themselves, doing what you suggest but absorbing the oil in the absolute minimum amount of cat litter (or "Spill Sorb" which is effectively the same thing) necessary, bagging it up, and paying a nominal amount (Oily absorbents are around £85 per 205l drum in today's market, so I'd expect to pay no more than £15 for a single rubble sack full) to get it taken away by someone who can give them the right paperwork to prove it, would be the cheapest option.
Most tank cleaning firms would balk at actually cleaning a domestic heating oil tank as being too small and too awkward to access and advise that it's disposed of as is, they might be willing to come shift it and arrange disposal however.
Various oil recovery/Haz waste firms take them away intact for a nominal fee (£50-85 + transport) but that's literally to take it away either loaded on their truck or from a location they can easily pick it up with a "moffet" forklift.
Those firms will then cut them up, dig out the sludge for recovery (most oily sludge can be "cooked" to yield a decent amount of oil) and send out the plastic to a drum recycling company with their other contaminated plastic containers, where it's shredded, washed in hot caustic, then dried and granulated for sale to plastic recyclers...
Technically the HWRC's (local tips) should be collecting the empty containers for recycling in this way, but they know that if it goes into general waste which is destined for an Energy from Waste plant they will never get challenged on it.
If their waste actually goes directly to landfill (this is now really quite rare) then the operator is taking a big risk as landfill loads are frequently inspected and sampled by both the landfill operator and regulators, I know of at least one site which got huge punitive fines for exactly this behaviour.
Someone ought to mention that to the folk living around Fort McMurray - or any major international airport or motorway/highway or petrol/service station or....
There's a lot of money goes into remediating the land around failed underground storage tanks, and refurbishing old tanks and piping to meet modern environmental protection standards (usually fitting an internal liner to make them double wall) is also big business.
Airports, fuel forecourts, car washes and even large car-parks have to have rainwater and firewater interceptors to prevent spills leaving site as standard these days; maintaining these unseen systems is probably the largest single activity within the workload of waste tankering and industrial cleaning firms, with domestic sewage coming in a close second.
(In case anyone was wondering how I know all of this, work for/on Waste Management projects makes up the bulk of my day-to-day, mainly chemical waste but also stuff for recycling and landfill leachate management)
