It isn't an under the table thing, at least in the UK. For the generalloy used frequency bands for this, there was an auction for the spectrum. You can get access to parts not being used by the people who bid on it.
You can also get an amateur radio license, and use frequency not normally used for this, but that probably means using SDR as most devices designed to use LTE will only work on normal LTE bands etc.
No bribes, connections, or anything shady etc needed.
There's also around 400 MHz of dedicated sharing-only spectrum in mobile bands, available in the UK at a flat price per 10 MHz required.
(Replying to GP)
At least in the UK, no bribes or envelopes of cash required. Nobody is going to want to help someone try to get started from scratch, but the spectrum access isn't anything like what you fear, at least in the UK. No connections required, the forms are all available online, and if you ask nicely and want bulk licences, you can use a spreadsheet instead for your requests, which is a bit less hassle than PDF forms.
You can also get an amateur radio license, and use frequency not normally used for this, but that probably means using SDR as most devices designed to use LTE will only work on normal LTE bands etc.
No bribes, connections, or anything shady etc needed.