Will the 4G LTE used in an iPad bought in England also work in Sweden? If I buy a new iPad with 4G LTE in the United Kingdom, will the 4G LTE work in Sweden (with a SIM from a carrier offering 4G LTE obviously)?

I am asking not least because of statements in this article that 4G LTE uses different bands in different countries.
No.
The LTE standard uses different frequencies in the US and Europe. However, the model sold in Europe is the US model. This has been officially confirmed by Apple [1, german].
LTE in the iPad
The iPad supports only the frequencies 700 and 2100 MHz [2] for LTE use. These frequencies are not used for LTE in the EU.
If you take a look at the footnotes, Apple states on their website (US and foreign) that:

4G LTE (is only) supported on AT&amp;T and Verizon networks in the U.S.; Bell, Rogers, and Telus networks in Canada.

LTE worldwide [3]
The following frequencies aren't really such even numbers. They are frequency bands that spread out over a whole spectrum of which little fragments are divided among carriers.

USA: 700, 1800, 2100 MHz
Canada and Mexico: 1800, 2100 MHz
European Union:  800, 1800, 2600 MHz * (bands in use differ widely)
Asia in general: 1800, 2600 MHz
Australia: 1800 MHz

There also exists this table [4] which lists very detailed information on frequencies bands used world wide. You can see here that the the 2100 MHz band is used for UMTS and IMT (= 3G standards) in Europe. The 700 MHz band does not seem to be used by carries in Europe.